What do Power, Technique, and Graffiti stats do?
According to the Dreamcast Manual, they are as follows:
POWER the amount of stamina
TECHNIQUE the larger the gauge, the smaller the turning circle
GRAFFITI the larger the gauge, the more difficult the graffiti and the less amount of cans you can carry, but the greater amount of points
I'm not sure if the graffiti stat determines the number of cans for every character or if there are exceptions.
The internet has trouble deciding what technique means (1) (2) (3). Some say it increases combo points. However, this may simply be that it's easier to get good combo chains using characters with better technique stats. According to the manual, it only affects a character's turning circle. Characters may have individual speeds, jump heights, hit boxes and trick difficulty.
These stats affect a lotta things in the game, and picking the right character can help you out a whole lot, depending on what you're trying to do.
POWER is just health. The higher the Power, the more damage the character can endure. If you're new to the game, you might want to opt for a character with medium-high/high Power while you're getting used to the controls. Most characters with high Power are usually (but not always) able to hold a lotta cans, and have simple graffiti tag combo patterns too.
TECHNIQUE is dependent on tricks and stunts you do. The higher the Technique, the more points you'll earn for pulling off a trick/combo. Points affect your rating at the end of each level (with the exception of the Jet Crush missions), which is why the stat is important to take note of. From personal experience, characters with higher Technique feel easier to control and make it easier to get to tricky or hidden spots, but I have no idea if the stat affects this or not.
GRAFFITI is dependent on graffiti and graffiti tag combos. The higher the Graffiti, the more points you'll earn for tag combos, but the harder the patterns will be. This stat is just as important to take note of as Technique, since it affects the ratings you get at the end of each level. There's seems to be a correlation between Graffiti stat levels and the amount of paint cans a character can hold; however, I'm not sure if this is exactly true, since some characters don't follow this pattern.
I've beaten JSR's Story Mode over 10ish times and have unlocked everything that can be unlocked (including the Steam achievements for the HD Remake), and I'm mainly vouching from my own experience. There are probably more in-depth and better explanations the one I just gave, but I hope it helps.