A vacation is defined as "a general leave of absence from a regular occupation for rest or recreation." As the PPC uses the term, though, the definition runs more like "a mythical, nirvana-like state in which the console does not beep and is not, in fact, present at all."
While the PPC Manual says vacations were frequent during the reign of the Mysterious Somebody, they are now infamously rare. Some agents believe they are impossible to get, but they can be earned. Generally, this is done by either performing particularly well in a mission (recruiting new agents seems to help one's chances) or by pestering the Flowers until they offer a vacation just to shut the agent up.
Vacations aren't typically very long, and many agents (such as Jay and Acacia, on their visit to the OFUM) end up taking a "working holiday," but the time given is generally the agent's to spend; a temporary visit home or to a favorite continuum seems to be one of the more common vacation choices. Some agents use the vacation time given to recruit others, but it isn't known if this is a particularly frequent choice.