A force is a push or a pull that acts on an object because of its interaction with another object. Forces come from interactions, so they act between pairs of objects. Force is a vector quantity, so it has a size and a direction.
All forces are either contact forces or non-contact forces. With a contact force the two objects are physically touching. Examples are friction, air resistance, tension in a rope and the normal contact force from a surface pushing back on an object resting on it.
With a non-contact force the objects are physically separated, yet they still exert a force on each other. Examples are the gravitational force, the electrostatic force between charges and the magnetic force between magnets.
When two objects interact, a force acts on each of them. For example, a magnet attracts a nearby iron nail, and the nail attracts the magnet. Each force can be drawn as a vector arrow.