You already know that a charge can push or pull another charge. But saying “the two charges exert a force on each other” leaves a strange question: how does one charge know the other is there?
The electric field is the answer.
A charge changes the electromagnetic condition of the space around it. At every point, we can describe that field by asking:
If I placed a tiny positive test charge here, which way would it be pushed, and how strongly?
That gives us:
The field exists whether or not we actually put the test charge there.
