In fire and advance mode, the units spread out a bit, leaving space between troopers. When firing, the entire first rank will fire as one body, then reload. While doing that, the second rank will step forward through the gaps, and then fire as one body, and begin reloading. After that, the third will do the same. Once all 3 ranks ahve fired (the fourth may as well, I don't recall if it goes that deep or not), there are two possible occurrences. If on targeted fire mode (i.e. you click to attack a unit), they will form up and charge the unit you designated. If on untargeted fire mode, they will all run back to their initial starting position and fire again.
It's not incredibly more effective than normal fire in terms of casualties caused in normal heads up fight. More effective, yes, but not a huge crippling advantage. If fired into an enemy's flank or rear while they're engaged from the front, it seems to cause a lot more casualties. What it does, however, is provide a massive shock advantage. This is especially useful when charging militia with grenadiers, for example. the shock hit of the ranked fire, followed by the charge, will quickly break a unit.
One thing to note: it shortens the range of attack though, which is why it's not optimal for a defensive fight.
[This message has been edited by Gnarlyhotep (edited 03-04-2010 @ 01:25 PM).]