You route the output of tracks to group channels. It pretty much does what it says on the tin. You can group a number of tracks and control them as one track.
FX tracks are tracks for..well...effects. You can send tracks to to an FX channel, but you don't send the output. The output of the track will still go to the master bus, while also sending a signal to the FX track.
Example...
If you want to add reverb to a number of tracks, you create your FX track, and stick a reverb in it. Then you take, say, a guitar, and open up its track. On the right of where the EQ section is, there a bunch of sends (black rectangles similar to the inserts on the left). If you click on it, you'll see your FX track in there. Once you've selected it, there's a blue bar at the bottom of the send. You can alter that to set how much signal goes into the FX channel.
When using sends like that, generally, the effect you use will want to be set to 100% wet, because you already have the dry signal going from the track to the master bus. Then the FX channel is only outputting the effect, rather than the combination of the dry signal and effect. That way, you can alter how promenant the effect is with the volume slider on the FX channel.
FX channels are pretty useful if you want to send a whole bunch of stuff to one reverb or something like that. You could do it with a group track, and stick the effect on the insert, but that's kinda different. Insert effects are for altering or shaping the signal (like with compression for example), and occur pre-fader. Send effects are for adding to it, and occur post-fader. Generally with something like reverb, which naturally occurs after a sound, you'd want to send to an FX channel, thereby adding the reverb to the original signal, rather than shaping the signal with reverb.
That said, it's all horses for courses with music.
Sorry if this isn't explained too well. For something like this I'd prefer to try and put some screenshots and diagrams together for you, but I'm at work at the moment and don't have cubase to hand. If I have the time later I'll try putting something together.