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)

One common way is to use the term acting:

Joe Bloggs is Acting Chief Executive while our CEO Lucinda Bucket is out of the country.

The term implies that Joe Bloggs is Chief Executive in all but name, for a temporary period. It can be used as a normal verb too: "While I'm away, Joe will be acting for me."

This term also appears in the 25th Amendment to the US Constitution:

Section 3. Whenever the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that he is unable to discharge the powers and duties of his office, and until he transmits to them a written declaration to the contrary, such powers and duties shall be discharged by the Vice President as Acting President.