A video demonstration of it is here. Fast forward to 4:24 to watch how FADC works:
To explain what a 'Focus Attack Dash Cancel' is, let me explain what a Focus attack is.
You press Mid Punch and Mid Kick at the same time to do a Focus Attack. This lets you counter some singular hit attacks, like a Fireball or a straight punch/kick. Occasionally you could use it to block special moves, so long as it's a move that only hits you once (Note, this is based on my own observation; not sure if there's a focus attack that could block a multi-hit attack like Ken's Dragon Punch).
If you hold down the mid punch and mid kick buttons long enough, you will strike a far stronger Focus Attack. The stronger it is, the more likely you can get your opponent to crumple (they'll stoop over and fall down). The time where your opponent is stooping over and falling gives you a chance to juggle your opponent, or hit them again with either a special move or another regular strike.
You can improve your chances of hitting someone with a special while they are crumpled by dashing. You can dash in SF4 by pressing forward or backward twice on the controller (Virtua-Fighter style!)
Now this is where it gets tricky....it's possible to cancel your special moves with the focus attack, dash forward, and then do a special move. This is 'focus attack dash cancel'. Why would you want to do this? To get more damage in, of course! You could also do this if your opponent blocks the first attack; in a way, it can also be used as a counterattack after your opponent anticipates your first strike. Counter with a focus, then dash forward and attack with a special move. Granted, I've still not been able to do this. It seems pretty advanced; but it's nice to know it's in the game. It's something new to learn and master, which is just part of the fun.