Another vote here for the definitions section. One of the most important and easiest sections to go through, especially for a new umpire.
I personally would walk him through the process of a game, as far as mechanics and whatnot. Arrive at the field, change, walk onto the field, have a plate meeting then jog out to right field. So much umpire training, especially for new guys, never covers what a game day actually looks like. You could start with a hypothetical "Top of the first, nobody on nobody out" and have the first play be a ground ball to the infield.
The concepts I'd focus on for mechanics are starting positions A, B, and C, taking plays at first base, and a general idea of where you want to be as plays develop. For example if you're in C with a runner on third and 2 outs, get over to the first base side of the mound for the play at first.
Plate work obviously is a whole adventure where you can talk about foot position, the slot, TIMING, etc. But I personally wouldn't bombard him with abstract concepts that don't have a practical use until you've umpired a few games and understand why timing is important or why making sure the fielder held onto the ball on a tag is so important.
Most importantly, emphasize common sense, fair play, and to use his baseball IQ. I'm assuming if he's interested in umpiring he must have some interest in baseball. Knowing the situation and understanding things from a baseball perspective will help a lot as a new umpire.
Note for when you inevitably talk about timing: Please make sure he understands that timing is proper use of eyes and not "he caught the ball, one Mississippi, two Mississippi." It's "he caught the ball, his foot is on the bag, the ball is in his glove" etc.