Surf trim both sides will trim the quilt at the line (using the racetrack image above as a reference) and will keep both resulting sections of the quilt - what was one extruded quilt is now two. You could accomplish the same thing (in this example) by creating two separate extrudes or on of one half and then mirror... Splitting the surface and keeping both sides is useful (for example) in Master Model building techniques - a master has the overall shape of the design that you want and a split (both side trim) allows you to break out the separate parts - like a housing of a cell phone adn the battery cover and the screen bezel - they all share the same shape and interfaces.
-Nate