Is it safe to delete heapdump.hprof.old? I'm on a mac book air running OS X 10.9.2. I want to free up space. I see that a file called headdump.hprof.old is occupying a lot of space. Is it safe to delete it? What does it do?
Yes, it is perfectly safe to delete the file.

It is used by programmers in debugging errors in programs. If you're not a developer, not actively debugging that specific program, or not actively involved in a support request regarding a bug in that program - you won't need the file.