The under 25 age group LOVES it because their parents do not know what it is and can not helicopter over their online accounts- like in FB, twitter or Instagram .
The kids THINK it's private. That the snaps go away.
It is something the kids have that is completely their own. Few people over 26 even use snapchat.
They can pretty much control who does or does not see their snaps.
Most adults can't wrap their heads around it because the kids just snap completely sophomoric and ridiculously childish stuff that adults don't get the appeal of.
When the grow ups start infiltrating snap chat the kids will leave and it will morph into an advertising and sales business machine like facebook, twitter and Instagram have become.

Oh, yes, the sex element is a big factor too.