I have an Avid BB7 front disc brake on a cycle that appears to have a missing inner brake pad. The outer one and the butterfly clip are in place. What might account for this? The cycle is new to me.
As you say 'new to me' I can assume you bought the bike used or were gifted it. I think the simplest answer to why a pad is missing is: very poor maintenance by the previous owner. Really though, how the pad came to be missing is irrelevant, you'll have to replace the pads with a new pair in any case.
If you have used the bike with the pad missing, check the rotor to make sure it isn't damaged. You'll have to replace it if it is.
As the bike came to you with in a quite dangerous condition, and this seemingly was not disclosed to you, you should check the whole bike for other issues or missing parts. There are a few questions about inspecting a bike on this site
There's also some videos out there such as this one from Park Tool.
If you don't feel confident doing this, take the bike to a good local bike repair shop.