PEAK -- PEAK refers to a series of metrics designed to evaluate a player's value in some statistic - most often WARP or non-negative WARP (used by UPSIDE calculations) - over a series of consecutive seasons. It has had two variations. The one currently in use for UPSIDE on the player cards is the five-year variant referenced by Nate Silver:
The version of Upside that we’re using here is the peak-adjusted variant, which measures a player’s most valuable five-year window up through and including his age 28 season (or simply his next five years of performance if he’s already age 25 or older).
-- Nate Silver, 2007
Also used in some writings simply uses the next six seasons of a player's career.
In both cases, seasons which have yet to be played are projected using PECOTA instead of ignored, so young players will have the full complement of five (or six) seasons of data. See also: UPSIDE.