That's actually a pretty difficult question. I guess the best way to answer that is to say that any time a material is deformed or forced out of it's natural, at-rest state, the deformation falls into 1 of two categories: elastic or plastic.

An elastic deformation is defined as one where the material will return to it's original shape after the force has been removed, while a plastic deformation causes permanent change in the material.

Imagine squeezing a rubber bouncy-ball...after you squeeze it, the ball returns to it's original shape. This is an elastic deformation. If you were to try the same thing with a ball of clay it would not return to it's original shape. This is plastic deformation.

This can also be seen by bending a pen or a pencil. A slight bend and it will recover it's shape but if you go too far it will either break or stay bent. This is another important point. Most materials have both an elastic and a plastic range of deformation, meaning initially the deformation is elastic but if you push them too far the deformation will become plastic.

Springs are specially designed to permit large amounts of elastic deformation. The first element of this design is the coiled shape that you see in most springs. This shape allows the spring as a whole to either be compressed or stretched very far while each section of the spring only undergoes a small change in shape. In this way, large deflections are possible but the material stays within the elastic region of deformation. Springs are also made of special materials, usually spring steel, which are designed to undergo large elastic deformation.

The last thing I might point out is that any spring will deform plastically if pushed too far. This is easily seen in the small springs in some ball-point pens if you pull on them rather than push them.