Have you seen the "Legally Blonde" movie? There's a good description of "snap" (in the "Bend and Snap" scene) - and this meaning is not present in any dictionary, I'm almost sure!

Seriously, there are two main types of fibers in connective tissue: collagens and elastins. Collagens are stronger, more difficult to "break" but are not highly elastic - cannot extend a lot.

Elastins are highly elastic - they can extend a lot, but are not structurally strong. That's why they are called elastins, and that's what your sentence is about.

They supply stretch capabilities and flexibility to connective tissue.

Hope this helps!