Your dough's ability to spring back to its original shape after being stretched -- the "rubber band" quality.
Elasticity comes from the glutenin proteins in your flour linking up into strong, springy chains. High elasticity means the dough resists stretching and snaps back when released. It's highest right after kneading and decreases during fermentation as enzymes and bacteria break down gluten. You need some elasticity for structure, but too much makes the dough hard to shape and prevents the yeast from inflating it easily.