A lot of things can be said about the predicate: that it contains the complements of the subject, that it is the set of words to add sense to the subject, that it adds meaning to the whole sentence, that it is essential for a sentence to have a meaning, that it contains the action done in the sentence, etc. but what it is always true of all predicates is that there is no meaning in a sentence without a predicate.
Analize this simple sentence:
My mother <u>works in a bank.</u>
subject + <u>predicate</u>
if we separate the subject and the predicate and state them alone, which one conveys more meaning and therefore is more important?
if we say "my mother." we say practically nothing and we cannot imagine what could be next in meaning.
but if we say "<u>works in a bank"</u> we can guess who the subject is and then guess the whole meaning of the sentence.