Simple Definition:

The subject in grammar is the person, thing, or idea that performs the action or is being talked about in a sentence. It is usually a noun [a word that represents a person, place, thing, or idea, including names of people] or pronoun [a word used in place of a noun].

Examples:

1. John is eating an apple. (Here, "John" is the subject because he is the one performing the action of eating.)
2. The car is red. (Here, "the car" is the subject because it is being described.)

Very Simple Definition:

The subject in grammar is the person or thing that does something or is being talked about in a sentence.

Very Simple Examples:

1. John is eating. (Here, "John" is the subject because he is doing the action of eating.)
2. The cat is sleeping. (Here, "the cat" is the subject because it is being talked about.)