A force never acts on its own. It is always part of an interaction between two objects, and each object feels a force. If you push a wall, you exert a force on the wall and the wall exerts a force back on you. If a magnet pulls a nail with a force of 2 N, the nail pulls on the magnet with a force of 2 N too.
The two forces in an interaction pair are the same type of force, equal in size and opposite in direction. They act on different objects, which is why they do not cancel each other out. The Earth pulls on a person with the force we call weight, and the person pulls on the Earth with an equal gravitational force in the opposite direction. The same idea works for contact forces (you push on the ground and the ground pushes on you) and for electrostatic forces between two charged balloons.
