A force never acts alone. Whenever two objects interact, each object has a force on it. These two forces are called an interaction pair. They are equal in size, opposite in direction and the same type of force.
The important point is that the two forces act on different objects. When you push on a wall, your hand pushes on the wall and the wall pushes back on your hand. A swimmer pushes the water backwards, and the water pushes the swimmer forwards. The Earth pulls a falling ball down, and the ball pulls the Earth up with a force of the same size. Two magnets pull on each other with equal forces.
Because the pair acts on different objects, the two forces never cancel each other out. Be careful with a book on a table. Its weight and the normal contact force from the table both act on the book, so they are not an interaction pair. The pair for the book's weight is the book pulling up on the Earth.
