If you are doing all of a persons work and have all their reponsibilities, especially for an extended period of time, you are either a substitute or a replacement. If you are representing them to the outside world for a short period while they are away and don't have their full authority, you are a deputy. This is the terminology used in most of the American firms that I have worked with.

I would say "I am substituting for my boss or colleague" or "I am standing in for him/her while he/she is gone" If it's the boss, you can say (if you want to show power), "I'm in charge in the boss's absence."

These are all correct. Another case, if you were substituting while a new replacement for someone who had left, is 'interim' "Jane Miller served as interim police chief in 2008." And let's not forget the old term from monarchy: regent. "His cousin Edward served as regent until James was old enough to take the throne." So there's your opportunity to make a joke in english- you can refer to yourself as 'regent', thereby exagerating your temporary importance as well as the bosses' normal majesty. OK, maybe not a good joke...