Truncating is deleting the unused part of a sample you probly recorded when your samplin. If you wanted a piano tone and you started recording a second too early, the 1 second before the piano is still taking up space in your memory. When you truncate, it deletes the unused sounds.
Im sure somebody could explain the MPC way of truincating better then me. But on the ASR10, go to the editing screen and select the wavesample you want to truncate. Then go to the EDIT>INSTRUMENT>WAVE page and make sure you hasve your start and end points where you want them to be. Then go to COMMAND>INSTRUMENT>WAVE and scroll over until it says "TRUNCATE WAVESAMPLE". Then press yes. It will say "PROCESSING" or somethin like that, then it will say "COMPLETED" or somethin like that.
NOTE: If you try to truncate and it says "NO WS SELECTED" it just means you need to select the wavesample you want to truncate first.