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This is something that I first heard about at last night's chanting, which was in Pali, but they had an English translation available for me. However, even the monks seemed unsure about what it was when I inquired. So here's what my research this morning found:
That another term for it is a "Pacceka Buddha" -- one who has been able to abandon greed, hate, and delusion in a time in history when there is no “real” Buddha teaching (for example, Siddhartha would be a "real" or "ultimate" Buddha). However, a silent Buddha is still somewhat limited in his wisdom, so he cannot start the type of teaching/scriptures that a "full" Buddha (such as Siddhartha) started. Therefore he remains a silent Buddha.
I also read that Buddha advised those he taught that in order to find "salvation" it is not necessary for each and every person to wait until full Buddhahood is gained. That aspirants can also find salvation by becoming Silent Buddhas -- which apparently is the same as a term I have heard used more in Thai Buddhism -- Arahants -- Perfected Ones. That a Silent Buddha is Enlightened, but not to the degree of a Supreme Buddha; they may still experience Nibanna. They do not preach to lay people (hence "Silent Buddha"), and they lead a life of relative solitude. That arahants have overcome their desires and other human weaknesses.
At least that's what I got out of some online sources.