Elasticity is the ability of the dough to spring back and have tension. If dough has too much elasticity it is called bucky. Bucky dough springs back into it's former shape as soon as you stop working it. If you roll a bread braid or Challah strip, it springs back.
For dough to rise it has to have a balance of extensibility and elasticity so it can stretch to a larger size and be elastic enough to hold and trap the rising gases.
If you have dough that is too elastic, this can be tamed by using active dry yeast instead of instant dry or fresh yeast, by using sourdough as a riser, or by letting the dough rest for 20 or 30 minutes.