@Whit If you send it to one individual (or 3, 10 or whatever) it deletes after they view it. If you post it on your "Story" it lasts 24 hours and then it disappears. And by "disappear" I mean you can't see it anymore but we all know things don't really ever delete once online.
There is also a way someone can "screenshoot" your photo but the app will tell you when they do that, although there's really nothing you can do about it if they do. They can then share that image through Twitter, FB, etc.
I SnapChat with my kids here and there--mostly send selfies or short videos of what I'm doing. I post short videos of my day for my other photographer friends, especially if it's photo-related and I follow them for the same reason.