Well, it's not necessarily so much as to 'catch it before it leaves', but rather, a short shutter speed to catch it in one spot, rather than long speeds, which catch it over time, and then the subject will blur if it's moving.
If you do use a shorter shutter speed, you let in less light, so then have to compensate by opening the lens more (larger aperture). For some reason, a more open lens is a lower 'aperture number' (eg. f/3.5 is more open than f/5).
Oh and then, this aperture setting, in turn, will affect the 'depth of field' (as MTI said).. but you needn't worry about that nearly as much. So you see, everything is connected and eventually you'll be messing around trying to find a compromise between these things.
That pretty much gives all the basics you need, now it's down to you to take some practice shots.. Make a note of the settings you use for each shot, or you won't really get anywhere
Russ!