Think of it as having a picture or video conversation in <10 second clips. I don't think that is a fad. That is just a slick form of communication for something that was slightly annoying to do.
This is where Snapchat does extremely well. It makes the act of sending a picture or video as frictionless as possible. I've never sent a video through MMS, but I've probably sent over 200 Snapchat videos.
It's not like sending an MMS with video or pictures is hard, it just isn't as dead simple as using Snapchat.
Another thing people like to harp on is the fact that people can take screenshots, thus "defeating the purpose." Fair point, but I think people who say this haven't really used Snapchat and don't really get why it is so sticky.
Sure, one of my friends may screenshot a silly face pic I send, but that's happened maybe 10 times out of the 4k+ snaps I've sent. The fact is I know I am not leaving a huge digital trail compared to using SMS/MMS, FB, GroupMe, etc.
Even if the system isn't perfect, it is good enough for me to trust. And the whole interaction model encourages me to send more pics and videos than I would send to my friends before I used Snapchat. It's almost replaced text messaging for me. Why send a text to my friend that I'm hungover, when I can send an image or video with my tired looking face and overlay text and drawings. It's so much more expressive and interesting than a text.
Another reason I like Snapchat is that I don't keep in touch via SMS with a lot of my friends. I may text them only once a week or every couple of weeks, but with Snapchat, I may send them a pic of something funny a couple times a week. Snapchat has made sending pictures and videos as frictionless as possible, and has changed how I communicate with people (I'm serious here).