I know health is how you know if a player will get injured or not.  But what does durability measure, then?

Durability is how much he can play.

For Pitchers it determines how far into a game he can pitch. For hitters it determines how many PAs he can handle without getting fatigued.

A hitter with a 90 DUR should be able to play almost every game, a hitter with a 75 DUR, for example, will need days off periodically to remain at 100%.

Posted by mchalesarmy on 1/16/2013 11:52:00 AM (view original):
Durability is how much he can play.

For Pitchers it determines how far into a game he can pitch. For hitters it determines how many PAs he can handle without getting fatigued.

A hitter with a 90 DUR should be able to play almost every game, a hitter with a 75 DUR, for example, will need days off periodically to remain at 100%.

For pitchers, I think you are confusing stamina with durability. 

Durability for pitchers is how often they can pitch, and how quickly they recover from fatigue between appearances.

You are correct. My mistake.

DUR for pitchers roughly equals recovery points during off days.

Thanks for the correction.

For position players, you can think of it as a rough percentage of 9-inning games they can play at 100%.