The subject is what's doing the action of the verb.
Examples:
(1) A box of pasta sits on the counter.
The box is the subject, and sits is the verb. The box is sitting.
(2) The cat chases the mouse.
The cat is the subject, and chases is the verb. The cat is chasing.
The verb agreement has to do with the fact that the subject and verb have to be in the same tense. If the subject is singular, then the verb must be singular. If the subject is plural, then the verb must be singular.
Singular:
She raises her hand.
Both the subject (she) and the verb (raises) are singular.
Plural:
We raise our hands.
Both the subject (we) and the verb (raises) are plural.