Vac here is a short, casual word for a university holiday — the weeks when there are no classes, between terms. "During the vac" means during the university break. This use is British, and it is narrow: it belongs to students and staff at British universities, especially the older ones like Oxford and Cambridge, where you hear "the long vac" for the long summer break. Outside that world people say "the holidays" or "the break". It also sounds somewhat dated now; younger students often just say "the break" or "the summer". You will still meet it in novels about university life and in college handbooks. Be careful, because the same three letters do other jobs. Vac is also short for vacuum cleaner in British homes — "give the floor a quick vac", and as a verb "I've vacced the stairs". And in American English vacay (not vac) is the casual short form of vacation. So the same short word points in different directions depending on who is speaking and where.