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A statement which can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory.
According to the Nobel Prize-winning physicist Richard Feynman 
(1985), any theorem, no matter how
difficult to prove in the first place, is viewed as ``Trivial'' by mathematicians once it has been proven.
Therefore, there are exactly two types of mathematical objects: Trivial ones, and those which have not yet been
proven.
See also Axiom, Axiomatic System, Corollary, Deep Theorem, Porism, Lemma, Postulate, Principle, Proposition
References
Feynman, R. P. and Leighton, R. Surely You're Joking, Mr. Feynman! New York: Bantam Books, 1985.