Newton's third law appears to be simple yet its content is subtle and easily misunderstood
Every force has an equal but opposite "reaction" force :
As Newton wrote himself : "What ever draws or presses another is as much drawn or pressed by that other." It is important to keep in mind that the action and reaction forces operate on different bodies. If this were not so nothing could ever move because forces would all cancel out. What is being pointed out is for example that as I push on this wall the wall experiences a force from my hand but also my hand experiences the same but opposite direction of force from the wall.
Another example
is shown here. I place a heavy brick on this ruler. First we analyze the
problem from the point of view of the brick. It experiences the force of
gravity,
The brick is also in contact with the ruler and so there is potential
for a contact force there.
Since the brick is clearly not accelerating the contact force must
exactly cancel the force of gravity.
That force we call the normal force,
The name comes from the fact that the normal force is always perpendicular
or normal to the surface which supplies it. 
is
not a reaction force to 
in the sense of Newtons third law because it
also acts on the brick. The reaction force to acts on the earth
as a whole since it is the earth as a whole which gives rise to the
gravitational force.
Considering the ruler it pushes the brick and hence it is pushed by the brick. In other words the ruler experiences the reaction force to the normal force. The ruler in turn is in contact with the earth which supplies normal forces to the ends of the ruler. The result of this combination of forces acting on the ruler is that it deforms elastically: Thus there is a visible sign of the fact that the ruler feels that reaction force to the normal force it supplies to the brick.
How about our poor earth? Is it going to accelerate because of the forces involved here? The answer is no because the forces all beautifully cancel out: The earth feels the reaction force to the gravitational force on the brick and is subject to the reaction forces to the normal forces it supplies to the ruler. But these are equal in magnitude and oppose each other and hence there is no net force on the earth due to our little experiment.
You should notice here the importance of identifying which object we are adding up the forces for. Newtons laws hold for any object we might choose to apply them to but we have got to keep clear to ourselves which object we have in mind! Newtons law of reaction is important when we consider the two bodies which inevitably are involved in establishing a force. It is counter-intuitive to most because it puts the parties involved in establishing a force on a completely even footing. It is hard to accept that the cart pulls the horse as hard as the horse pulls the cart but that is nonetheless the way it is!
