There's a pretty nifty article linked from the Wikipedia article on the Emotion Engine that discusses the details in the "Emotion Is the Difference" section on page 2:
But much of the EE’s compute power will go toward an even loftier
goal: behavioral synthesis, or, as SCE calls it, emotion
synthesis. This technology gives game programmers the ability to
accurately model all manner of physical systems, allowing realistic
behavior of characters and objects. For example, the system will
enable lifelike facial expressions
There's another description in this paper:
Emotion synthesis means the real-time synthesis of a computer graphics
animation scene that projects a great deal of atmosphere. For example,
when a female character walks into a video game scene, her motion must
be determined by solving physical equations in response to interactive
events instead of replaying prerecorded data. Moreover, differential
equations with a large number of variables must be used to describe,
for example, the waving motions of her hair in a breeze. For
authenticity in emotion synthesis, the CPU must execute these
calculations in real time.
As far as I know there is no actual behavioral synthesis or emotion synthesis technology used in any PS2 games. It's a generic way of saying "We have a lot of computing power so games will be more realistic". But for marketing purposes it makes a snazzy name that implies there's some special functionality to the EE that competitors don't have.