What do you call it when someone assumes the job of someone else who is out on vacation?

You could say that person B is standing in for person A:

to act as a stand-in (a person or thing that takes the place of someone or something else for a period of time (from M-W.com)

or that they are covering for them:

To act as a substitute or replacement during someone's absence (also from m-w.com, v.i. def 2)

or that they are substituting:

to put or use (someone or something) in place of someone or something else (m-w.com again)

A temporary replacement / substitute?

A locum:

A locum is a person who temporarily fulfills the duties of another. For example, a locum physician is a physician who works in the place of the regular physician when that physician is absent, or when a hospital/practice is short-staffed. (http://en.wikipedia.org/wiki/Locum)

In various committees and other voting bodies, it is common to designate an alternate. In case the primary officeholder is not available, the alternate will fill in.

In American English, several positions use the prefix "co" to indicate this. E.g. co-pilot (fully capable pilot that works when the pilot is unavailable) or co-manager (often in retail, a manager that has all the same duties as the Manager but who may defer if they are both there at once).