Chase
Chase is a function that makes sure your MIDI instruments sound as they should when you locate to a new position and start playback. This is accomplished by the program transmitting a number of MIDI messages to your instruments each time that you move to a new position in the project, making sure all MIDI devices are set up correctly with regard to program change, controller messages (such as MIDI Volume), etc.
Example
You have a MIDI track with a program change event inserted at the beginning. This event makes a synth switch to a piano sound.
At the beginning of the first chorus you have another program change event which makes the same synth switch to a string sound.
You now play back the song. It begins with the piano sound and then switches to the string sound. In the middle of the chorus you stop and rewind to some point between the beginning and the second program change. The synth now still plays the string sound although in this section it really should be a piano.
The Chase function takes care of that. If program change events are set to be chased, Cubase tracks the music back to the beginning, finds the first program change, and transmits it to your synth, setting it to the correct sound.
The same thing can apply to other event types as well. In the Preferences dialog on the MIDI page, the Chase Events settings determine which event types are chased when you locate to a new position and start playback.