Put simply, the CoX Day Job system allows players to log out from a specific location (like a hospital or vault) and when they return to play, after an extended log out period, they will gain a temporary power or some other benefit. With the exception of badges and accolades, the benefits either last for a limited time or have a limited number of uses before they are used up. However, you can replenish the benefit by logging out in the same area. Most rewards need 10 days of logged out time to hit the maximum benefit.
There are a total of twelve possible logout locations for Heroes, and the same number for Villains. For example, a Hero can work as an Intern by logging out in the lobbies of Portal Corp, with the associated reward being a large inspiration on Mission Complete. A villain can work as a Demagogue (maybe 'work' is the wrong word here - it seems everyone else would do the work in this case) by logging out in the Arachnos building in Port Oakes, and would get an Influence reward on Mission Complete in recompense.
The rewards seem surprisingly generous, with many adding something extra on Mission Complete; and yes, there is a Bonus XP reward, for working as a Law Enforcer or Arachnos Agent. Once a character has been logged out at a given location for a total of 30 days, which of course needn't be consecutive, they earn a badge associated with the Day Job. Earning a badge increases the rate at which characters earn benefits, as well as the potency of these benefits.
Earning multiple badges, as we knew, unlocks Accolades. You gain an Accolade by earning two Day Job badges that work together. For example, you unlock the Police Chief accolade by earning the Law Enforcer badge along with the City Official badge, and that in turn grants a Baton power (smashing damage and a chance to stun). So players don't have to guess, each Day Job badge you earn gives you information about which badges you need for which associated Accolades. Some of the powers look formidable: AoE hold, Ally Resurrect, Ally Heal. They can be 'recharged' by logging off in the location associated with one of the contributing badges.
As if all of this wasn't enough to whet appetites, City of Heroes/Villains is also including a form of rested XP. Every character is considered to be 'On Patrol' (or the villain equivalent) after they log out. Logging back in earns you one bar of double XP for defeating enemies for every 24 hours spent logged out, up to a total of 10 bars of double experience. The double XP shows up as a blue portion of the XP bar. XP debt, if applicable, is burned off first before any double XP is applied.
Players are prompted when they're in a Day Job location. For example, on visiting a hospital, you'd see an icon appear under your health bar. So, it won't take characters long to find themselves a suitable Day Job; and there are also costumes associated with them.
It may seem odd to want to reward players for being logged out, but City of Heroes encourages 'altitis' more than any other game we've known. You can't play all your characters all the time. Although badge collectors would probably find it nigh impossible to collect all the badges on a single character, this looks like a very original way to keep players rotating the characters they play, check on characters they haven't played in a while, and add some depth to their character concepts.