Rubber bands are made of long polymer molecules. These are all tangled together, and you could think of them as being similar to a bunch of interwoven springs. The polymers can be stretched to a more extended state, which is what allows a rubber band to stretch without breaking. More accessible configurations exist, however, when they are in a more contracted state, which means that the more contracted states have higher entropy (see “Physical and Theoretical Chemistry”) and for this reason are more favorable. This is what makes the rubber band want to contract and is what gives rise to its elasticity. (Check out “Polymer Chemistry” for more questions on polymers.)