A predicate symbol describes or relates. Like an adjective (”… is mortal”) or a verb (”… loves …”), it says something about the objects named by terms. Applied to terms, it produces an atomic formula — a claim that can be true or false.
Under a structure, a predicate becomes a concrete relation. asks: is in the Mortal set? asks: does the pair belong to the Loves relation?
The grammar is primitive but the idea is familiar: nouns name things, predicates say things about them. First-order logic just makes this distinction formal.