Tapering is basically where the athlete 'eases off' the training in the days leading up to an event, so as to be in peak physical fitness for the event.
Kind of what I am doing regarding studying right now...
Conditioning, as in in a training session, refers to 'conditioning' the body; that is, improving general fitness, so as to prevent injury, and increase performance when it comes to the event / activity being trained for.
This is very much 'dumbed down' but I hope it helps...
Good luck tomorrow all!!