An attainment is a something a character receives for in character success that identifies a remarkable acheivement or unusual relationship. Sample attainments might be
Trusted by the Mayor: You've proved yourself in the eyes of the mayor of Daunton; he trusts you with important or sensitive assignements. This attainment can be lost by betraying that trust, having it revealed that you've acted against the interests of the town.
Explorer of the Shadowrift: You've visited the Shadowrift on Kithria and lived to tell the tale
Caught the Skingraft Slasher: Your were part of the group that revealed the slashers identity and help capture her

Attainments would be approved in advance by judges (usually as part of an adventure submission) and awarded by DMs on an individual basis.

... some attainments could have trivial mechanical benefits
these should be granted as the result of success in a significant adventure or series of adventures
so if you're "known to be a friend of the Peg-legged Don" you get +2 to intimidate and diplomacy when dealing with the merchants of Bacarte; +4 when dealing with members of the Don's family
... rare attainments could have non-trivial mechanical benefts
these should be capstones at the end of a truly epic and difficult adventure
so if you've "Helped seal off the Caverns of Madness" you get +2 to saves vs effects with the psychic keyword; once a day as an immediate action when effected by a condition caused by a power with the psychic keyword that a save ends you may make a saving throw
... affliation attainments would connote a particularly close relationship with a group
similar to affiliations, which were sort of halfheartedly implimented in varous 3.x suppliments. You might get a discount on certain items or services, access to unusual equipment (alchemy?), or even the "lend" of a certain kind of magical item.
So the "Defenders of Allaria" might give senior members the lend of a "battle standard*" magic item of level equal to the characters
(*=WotC just put it out on the web; it's not approved content for L4W but it's an easy to understand example)

Advantages may include

  • An easy way for DMs and other players to find out what you've accomplished
  • Could spark ideas for cross linked adventures
  • A way to reward roleplaying
  • With the advent of a pretty remarkably potent reward system for DMing we'll see a lot of higher level characters in play who didn't get there by playing; attainments are only available through actual play. A 4th level character who advanced normally will potentially have a lot of attainments (relationships, etc) that a character who "got to 4th on points" won't be able to match

Disadvantages include

  • Bookkeeping
  • Judge workload
  • Possible balance issues if we have mechanical effects