Depreciation usually refers to the loss in value of a tangible asset... a car, a piece of equipment, a plot of real estate. The asset loses value over time, and that "loss" is included in a business' balance sheet.
When Veeck bought the Chicago White Sox in 1959, he made the assertion that ballplayers "waste away" over time, and claimed depreciation of the value of their contracts on his taxes. The Internal Revenue Service, remarkably, bought it. Since then, owners of pro sports teams have been able to use the so-called "roster depreciation allowance" to offset profits and gain a tax advantage.
And if you think treating ballplayers like livestock - even for tax purposes - is decidedly creepy, you're absolutely right.
The roster depreciation allowance does have limits; it can only be used on deals in place when a team is purchased. So new Detroit Pistons owner Tom Gores will be able to claim roster depreciation on the contracts of, say, Charlie Villanueva and Richard Hamilton, but owners that have been in place for longer will not.
Update: I am informed by Tim Donahue of Eight Points Nine Seconds that the audited financial information submitted by the league as part of the CBA negotiations excludes the roster depreciation allowance.