The term comes from the Latin predicare “to say about”. Predication is what is said about something, or the process.
In the simple sentence, “Peter Carlo is delightful“, the quality “delightful” is a predicate (said) for a person. The word or expression spoken about something or someone is called a predicate (in this example “delightful” is a predicate), the object or the thing that is said about is a subject (Peter Carlo in the example).