The predicate in a sentence is simply the part of the sentence containing the verb. Usually (in a simple sentence) the last part of a sentence. Such as Peter's dog swam in the river. "swam (verb) in the river" is the predicate.
Predicates modify sentence subjects.
"John ate the meat quickly"; "ate the meat quickly" is the predicate.
"Icelanders are hardy"; "are hardy" is the predicate.
"I won"; "won" is the predicate.
