In grammar a predicate is a part of a sentence. More particularly, the predicate is further information about the subject - what the subject is doing, what the subject is like, etc. It's really that part of the sentence which is not the subject! See sentence (linguistics). As a verb, to predicate means to state, imply, or make an assertion about something.
In Bertrand Russell's theory of types, a predication is an act of typing, that is, assigning a type. A definite description in fact contains a claim of existence.