Snapchat is a photo sharing app that lets people send self-destructing messages. It's a fun way to send a message to someone when you don't really have much to say.
Last year, Snapchat reportedly turned down a $3 billion buyout offer from Facebook. At the time, people were incredulous. Since then, Snapchat has continued to grow, making the company's founders look wise for not selling to Facebook.
Facebook, meanwhile, has tried and failed multiple times to create Snapchat clones.
One of the reasons Snapchat has taken off is that it doesn't create a permanent record for users. As Facebook has grown, it has become a more formal. It's no longer a place to goof off and show yourself, say drunk, or doing silly things. Snapchat with its disappearing photos is a more relaxed space.