Ton,
Insert DSP's can be assigned (or inserted) to individual voices to modify their Timbre, Distortions (eg. for guitars) , EQ, Increased Presence, Dynamics (more live sound through use of compression), Modulation of various types, Delay (giving spatial effects to strings or solo wind instruments) Reverb and so on. For live playing they can be assigned to panel voices and style voices and the SX's 8 (if fully used) will need to be shared between them. If a song containing Dsp's is also simultaneously played there is still only a max of 8, so usually the keyboard will dynamically assign them as required and may "steal" them from other positions.
The above is not complete, it's probably best to work through the list of effects on the KB over time to find out what they can do. Usually trial and error and experience is needed to get optimum results. It is not a case of inserting a Dsp or two and suddenly finding marvellous results. It has to be worked at.
There are unusual Legacy effects which convert trumpet sounds into muted trumpets, and one is particularly useful for BigBand, providing transitions between smooth and trumpet stabs depending on velocity to accompany the main melody.
John