The subject of the sentence is what (or whom) the sentence is about.
In the sentence “The dog is running in the field,” the dog is the subject.

A predicate is the part of a sentence, or a clause, that tells what the subject is doing or what the subject is.
Let’s take the same sentence from before: “The dog is running in the field.”
The clause running in the field is the predicate; it’s dictating what the dog is doing.