A nullary predicate is a proposition. Also, an instance of a predicate whose terms are all constant — e.g., P(2,3) — acts as a proposition.
A predicate can be thought of as either a relation (between elements of the domain of discourse) or as a truth-valued function (of said elements).
A predicate is either valid, satisfiable, or unsatisfiable.
There are two ways of binding a predicate's variables: one is to assign constant values to those variables, the other is to quantify over those variables (using universal or existential quantifiers). If all of a predicate's variables are bound, the resulting formula is a proposition.