(Disclosure: I'm am old bastard myself but I work in the mobile dev world so it's my job to know when things are making waves in the industry.)
The demographic that they appeal to is very, very young. As in teens and college-aged adults. The app itself is extremely popular in the iTunes store and on Android. So much so, in fact, that Facebook, after not being able to buy it quickly (after explosive... truly explosive growth) decided to rip it off and build a clone called, wait for it, Poke.
People declared the end of Snapchat as big bad Facebook was going to eat their lunch, digest their user base and excrete them out into a paper bag to be lit aflame and left on Snapchat's front step. Poke hit around #14 on iTunes, then slide down fairly rapidly and is now an afterthought.
This was a victory for small dev shops that demonstrated that big companies can clone a product but that user loyalty is a very, very real thing.