Newton's Third Law states that every action has an equal and opposite reaction.

• When you apply a force $F$ on the wall, the wall simultaneously applies a force $-F$ back on you.
• These two forces constitute an action-reaction pair. They act on different bodies (you and the wall) and therefore do not cancel each other out on a single body.
• The wall doesn't move because your force is balanced by the internal stresses and the attachment of the wall to the ground/Earth, but the reaction force on you still exists.