ESAI stands for "Enhanced Strategic AI". It is an AI Commander Enhancement for Battlefield 2. It is a replacement for the default DICE commander script.
This is a shot of ESAI running in AI Debug mode, on the Forgotten Hope 2 map: Mount Olympus.
Note the top left corner-
Team 1 is using the strategy "axis_attackSouthWest", while Team 2 is using "counterAttackHardest3". The first strategy was custom written for this map; the second one is a part of the ESAI core strategies.
The Big Idea here is that the CO now has strategy options more advanced than the defaults.