The rabbis are saying that there is some truth in every dream.
They are also suggesting that dreams, like prophecy, ultimately come from a Divine Source.
Why only 1/60th?
Because the Divine Message gets transmitted to us through our own personal and cultural filters. Thus, God “spoke” to Mosheh and the later prophets in Hebrew because that was the language they understood. But Mosheh’s Hebrew is not entirely the same as Yirmiyahu’s/Jeremiah’s; language changes over time. God didn’t “speak” any differently. The filters had changed.
Where is the Divine Source of these messages? At the basis of our own minds:
“Transcendental Meditation is a process of experiencing consciously the subtle state of thinking and getting to the source of thinking, and the source of thinking is a reservoir of energy and intelligence…’Transcendental’ means: the mind…’transcends’ the experience of thought…gets through the…finest state of thought and thereby it is ‘transcending’ the field of thought. That’s why we call it ‘Transcendental Meditation’.” 
When I first learned TM and was told about a “source of thought,” it literally made no sense to me. I had never imagined that “thought” had a “source.” Thoughts filled my head quite on their own; they didn’t seem to come from anywhere.
This source of our thinking is Divine, whether we recognize it as such or not. The Rambam tells us that our existence is based on God’s Existence:
“The foundation of all foundations and the pillar of all wisdom is to know that there is a Primary [‘first’ or ‘fundamental’] Being Who brings all that exists into existence. All that exists only exists through His true Existence.
If the Creator did not exist then nothing else would, for nothing can exist independently of the Creator.” 
We can no more be separate from God than a wave in the ocean can be separate from the water that makes up the ocean.
God, the basis of our existence, is also the Source of our thoughts.
This is present in us as our “Inner Mind” or “Higher Mind.”
There is a long tradition in the Talmud of rabbis seeing and speaking with Eliyahu/Elijah, despite Eliyahuh’s having left this world hundreds of years earlier:
“Rabbi Yehoshua ben Levi met Eliyahu standing by the entrance of Rabbi Simeon bar Yohai’s tomb…” 
It doesn’t say explicitly that Rabbi Yehoshua was praying or meditating. But – Rabbi Simeon bar Yohai was associated with high spiritual attainment even in the Talmud (later honored as the source of the Zohar). Why was Rabbi Yehoshua at his grave? What was he doing while there? The suggestion that he was praying or meditating is strong. He “met Eliyahu” — cognitively, as the “Four who entered the Garden” were understood to have done so cognitively, not physically. Rabbi Simeon asks Eliyahu several questions about his own future and the Meshiach. “Eliyahu’s” answers are the responses of Rabbi Yehoshua’s own Higher Mind.
The medieval movement known as the “Hasidei Ashkenaz” has a rich tradition of individuals who have passed on coming to us in dreams, giving us new messages, insights or teachings:
“…I saw Jews in the Garden of Eden [while in a dream-like state]. I recognized one Jewish woman I knew. I noticed that her sleeve was stained with wax. I asked her, ‘Why is it that you look different from all the other women?’ The woman replied, ‘I once lit a lamp on Shabbat. That is why I have to suffer the disgrace that my sleeve is soiled with wax [while I’m otherwise living in Paradise]’.” 
A famous example, also from the Hasidei Ashkenaz, has to do with the prayer “Unetaneh Tokef” that’s recited on Yom Kippur:
“… on the third day after [Rabbi Amnon’s] sanctification [death as a result of torture by religious authorities] [Rabbi Amnon] appeared in a dream to Rabbi Klonimos ben Rabbi Meshullam ben Rabbi Moshe ben Rabbi Klonimos, and he taught him this prayer, ‘Unetaneh Tokef…’ and he commanded him to send it to the entire Diaspora, that it should serve as a testimony and a remembrance…” 
Rabbi Amnon had himself composed and recited this prayer — extolling Divine Justice and Wisdom in whatever form it appears in our lives — laying in his bed before the Ark on Yom Kippur. Then he died. The exact wording of his prayer was not immediately recorded. Three days later, he appears to Rabbi Klonimos (or Kalonymus) and causes him to learn it verbatim, to teach it to the Jewish communities of the world. It has remained central in Ashkenazic Yom Kippur liturgy since that time.
Did Rabbi Amnon appear to Rabbi Kalonymus? It’s a typical motif of the Hasidei Ashkenaz. But we can also understand that Rabbi Kalonymus’ own Higher Mind — which was the same as Rabbi Amnon’s — transmitted this message to him; “spoke” to him and “taught” him. Rabbi Kalonymus’ dream therefore had an aspect of “prophecy.”
Many stories are told of Rebbe Nachman of Breslav receiving visits from great Hasidic teachers of the previous generations, including the Baal Shem Tov. In one instance, the rebbe’s own mother visits him:
“…it was the evening of his mother’s yahrtzeit — the 19th of Adar. He had forgotten and had not lit a [yahrtzeit] candle or said kaddish. That year was a leap year and a yahrtzeit in Adar is observed in both months of Adar. During the writing of [the lesson ‘Nine Tikkunim”] his mother came to him and reminded him of the yahrtzeit. He immediately called a minyan…and learned from the Mishnah [as is customary on a yahrtzeit], said kaddish and lit a candle for her.” 
Note that it doesn’t say that the Rebbe remembered that it was his mother’s yahrtzeit. As he reported to his disciple, Rabbi Nathan of Nemirov, the Rebbe saw his mother — whether cognitively (in thought) or as an actual presence in the room isn’t clear. But I understand it as the Rebbe’s own Higher Mind reminding him of his mother’s yahrtzeit, appearing to him in a kind of waking-dream in the familiar form of his mother.
Just as you can never be separate from God, you are never separate from your own “Higher Mind.” It is there with you. It is there for you, even if you’re unaware of it:
“If I knew where the good songs came from, I’d go there more often. It’s a mysterious condition…” 
They come from our own Higher Mind; our own Higher Self. Not without some human effort, through which we grow in technique and experience. Yet, even an illiterate or semi-literate person can receive messages far beyond their experience:
“Srinivasa Ramanujan (1887-1920) had negligible formal training in mathematics. He died tragically young, aged 32. In his short lifetime he produced almost 4,000 proofs, identities, conjectures and equations in pure mathematics.
Although he died in 1920, the richness of his ideas and conjectures in fields such as Elliptic Functions and Number Theory – nearly all of which were correct – were ahead of his time, and continue to inspire and direct research carried out by mathematicians today…
Ramanujan said that the Hindu goddess Namagiri would appear in his dreams, showing him mathematical proofs, which he would write down when he awoke. He described one of his dreams as follows:
‘While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing’.” 
Did Ramanujan receive his mathematical equations from the goddess Namagiri? I would posit another explanation: They came from his own Higher Mind. Although the article says that he had “negligible formal training in mathematics,” other sources describe him as an autodidact (one who can teach himself). Even this receptiveness to and understanding of otherwise unfamiliar material could involve his Higher Mind. But his application of what he learned was, as he reports, received in dreams. The math he had previously learned formed a “filter.” “Namagiri” was also worshipped by his mother, which further helps explain the “filter” that allowed Ramanujan to receive the messages in a form acceptable to him.
There are many other examples of scientists receiving answers in dreams to the questions they were working on. 
Divine inspiration — רוח הקודש/ruach ha-kodesh — isn’t limited to religious or scientific themes:
“Everyone warned Desi and me that we were committing career suicide, by giving up highly paid movie and band commitments to go for broke on TV. But it was either working together or good-bye marriage! Ever try being married seven years out of ten by long-distance call and wire? Then I dreamed about Carole Lombard [Lucille Ball and Carole Lombard had been friends before the latter’s death in 1942]. She was wearing a very smart suit (Carole always dressed very beautifully) – and she said, `Take a chance, honey. Give it a whirl!’ After that, I knew for certain that we were doing the right thing.” 
Again: Did Carole Lombard actually visit Lucille Ball in a dream? I offer the same alternative explanation as I did before: It was Lucille Ball’s own Higher Mind advising her, filtered through a form that was familiar and acceptable to her — her friend, Carole Lombard.
As we’re never separate from our own Higher Mind, we can always seek guidance from it. But to do so requires the relaxing of all mental effort:
“The method was simple. A child could use it. Inwardly ask a question, then listen intently…” 
By “intently listening,” the author means: Stop trying to solve the problem by any effort of your Lower Mind. Ask, then wait patiently and quietly.
Our “Higher Mind” is not found by effort. Much the opposite. We receive our response when our Lower Mind is relaxed — as it typically is in sleep.
A dream might be “1/60th prophecy” — but it often need not be more than that.
 Talmud; Berachot 57b
 Maharish Mahesh Yogi, quoted in an interview at: http://www.trancenet.org/trtrop.shtml
 Rambam (Maimonides); Mishneh Torah; Book of Knowledge 1:1-2 (and elsewhere)
 Talmud: Sanhedrin 98a
 Rabbi Yehudah He-Chasid; Sefer Chasidim: The Book of the Pious, A. Finkel, trans.; Jason Aronson; © 1997 by Avraham Yaakov Finkel; p. 87
 Rabbi Nathan of Breslov [or Nemirov]; Tzaddik — A Portrait of Rabbi Nachman; Rabbi A. Greenbaum, trans.; Breslov Research Institute, © 1997; p. 139
 Leonard Cohen at:
He likens this to “the life of a Catholic nun. You’re married to a mystery”
for a longer and more thorough article about this man and his work, see:
source for this anecdote cited as:
Harris, Warren G.; Lucy and Desi, the Legendary Love Story of Television’s Most Famous Couple. (New York: Simon & Schuster, 1991)
 Crum, Jessie K.; The Art of Inner Listening; © 1975 by Jessie K. Crum; p. 14