The difference between compression and tension is that a compressing force causes an object to shorten in the direction of the force, while a tension force causes an object to lengthen in the direction of the force. Regardless of the strength of the material, compression and tension forces always cause some amount of deformation. Different materials deform in different amounts and return to their previous shape differently as well.
Compression and tension forces are very important considerations whenever a structure is being built or used. In general, any object has a tolerance for compression and tension, and exceeding these tolerances results in damage to the object. Such damage is either a permanent lengthening or shortening, a lateral bend or even a break, where previously continuous material is physically severed.
When an object such as a beam is being bent, it is actually subject to both compression and tension at the same time. The inner edge of the bend is shortening and subject to compression. The outer edge of the bend is stretching and subject to tension. It is common for materials to be stronger in compression than they are under tension, and materials with these features are called brittle. Concrete is a very common brittle material.