Predicate symbols are symbols used to denote some property of objects or some relation between objects. Consider the sentence
Max likes Claire
In FOL, we view this as a claim that the predicate likes expresses a relation between the individuals referred to by the names Max and Claire.
These individuals are called the "arguments". In this case, there are two.
A unary predicate with one argument denotes a property.
A predicate of arity >1 denotes a relation.