Spinsterwun beat me to it but I'll go ahead and post this anyway...
Well, you know how with a mixer you can turn knobs and pull sliders while the music is playing so that you can mix to a stereo master? How you can raise a guitar track up when its solo starts, and bring it back down when the vocals return? Automation simply means that those knob twiddles and slider slides can be recorded so that they can be repeated. It's potentially labor saving because with a real mixer and only one pair of hands there's only so much one can do during playback. Automation gives you as many hands as you need to make every tweak you want. (The other hand is that it makes mixing more labor intensive because if you can make every possible tweak you can imagine and fiddle with it in nearly infinite detail, you just might -- where in the old days, you had to live with the best you could do and make compromises).
Besides mixes being automated, parameters of a guitar effects box can also be controlled by recorded data, usually MIDI data. So as a song progresses you might want to change tones -- maybe a chorus on the chorus, flange and delay for the solo, that sort of thing.