Predicates are one of the building blocks of the sentence. They are similar to objects, in that they complete the subject-verb pair, but they are only used after certain verbs, such as to be, to seem, to appear, to become.
See the Note below on different meanings of this word.
Some verbs, such as to be, to seem, to become, can be followed, in both French and English, not only by a noun, but also by an adjective.
The block which follows such verbs is not an object but what is called a predicate (or attribut in French). Predicates are only found after the verb être and a very few others. Unlike an object, a predicate is closely related to its subject and the verb functions a little bit like an equals sign.
Compare the following sentences, where the block which follows the verb is an object. The object (l' and ses clefs) is independent of the subject, tells us nothing about it.
If the predicate is an adjective it must agree with the subject in French. So you say Sa mère est folle, but Son beau-père est fou.
Verbs which take predicates can also be accompanied by adverbials, so Sa copine semble un peu perdue ce matin contains four elements: a subject, a verb, a predicate (un peu perdue) and an adverbial.
Note: The term Predicate has another meaning. In this sense, the predicate is what is said of the subject.
In this sense, then, a sentence can be divided into two parts, the subject and the predicate. We will not be using this traditional meaning of predicate here.