Elasticity is the range of binding travel before it releases the boot. A high elastic and low elastic binding will release at the same forces (torques) at the same DIN setting. A more elastic, higher travel binding has more time to absorb energy, which, depending on the fall, may mean the difference between staying clamped in and a prerelease.
Consider the climbing world: There are dynamic ropes and static ropes. Dynamic ropes are designed to stretch under load, whereas static ropes do not stretch (much). Now consider the scenario where you are tied in to one end of a rope and the other end is anchored to the cliff above you. You then climb up 5 feet and fall. With the dynamic rope, as soon as you run out of slack the rope starts stretching slowing your fall, keeping the forces on the anchor, your belaying partner, and yourself comfortably low. Now do the same thing with static line (no, don't do it!). Because the static line has lower elasticity, when the line runs out of slack the generated forces are much, much higher, easily exceeding anchor and rope strength. Here's a fun article and video on dynamic loads on slings, comparing stretchy nylon to non stretchy dyneema and shows how easy it is to break the "unbreakable":
Translate this to alpine bindings: A fall with a more elastic binding could keep the forces below the release thresholds and you stay clamped in, whereas a less elastic binding would produce higher forces releasing the boot for the same fall. Note that both release at the same force so your bones stay intact regardless. It's just in one case you continue skiing and in the other you're tomahawking down the hill.