Bump was and early innovator in the area of file and contact sharing on mobile devices. Interest has waned a bit in recent years, but then Google bought the company back in September. Work seemed to stop on Bump's apps shortly thereafter, and now we're getting the official word – Bump and Flock are no more. Both apps will stop working and be removed from Google Play (and the App Store) on January 31st, 2014.
Bump was one of the first apps that made it easy to send files between devices without typing things in. You could just have two phones (geographically) close together and bump them to send files over the internet. Google has since taken up NFC as a more direct method of accomplishing the same thing. Flock was less well-known, but might have been more interesting to Google in terms of technology acquisitions. Flock is an automatic photo sharing app that recognizes faces and can share photos with the people it identifies in them.
If you have data in Bump and Flock, simply opening the apps will offer instructions for getting your data out. Don't procrastinate, though. All user data will be wiped after the shutdown date. The Bump team will go on to work at new projects within Google, but Bump has reached its end.