According to the context, a predicate can have two meaning.
In mathematical logic, a predicate is commonly understood to be a boolean-valued expression.
In grammar, a predicate is one of the two main parts of a sentence, apart from the subject, which the predicate modifies. For example, in the sentence "Albert is tall", "is tall" is the predicate. In linguistics, a predicate is an expression that can be true for something. The expression "is tall" is true for things that are tall.