The subject in grammar is the agent (the 'doer') in an active sentence such as: Alan kissed Jane.
However, there is a difficulty. The following two sentences are identical in meaning:
Only in the first sentence is our children the grammatical subject. So there is a difference between the logical subject and the grammatical subject.[1]p996 Also, many sentences have no subject, for instance:
If a sentence does have a subject, then the rest of the sentence may be called the predicate.