As far as I can work out, when you order a character to attack, this happens:
1. Pause for speed factor
2. Attack as many times per round as possible, with a relatively short pause in between attacks
3. Pause until six seconds after part 1 started.
4. Repeat, starting from part 1.
BGII is not actually turn-based. Notice how the pause in step 3 creates a sort of virtual round? As far as I can tell, these 'rounds' are not synced for different characters, and they do not have to do with the global 'pause at the beginning of each round' option (except that both are 6 seconds round). I'm not sure how moving and casting spells work with this, but I think that doing either makes you start again from 1, but doesn't allow you to get more attacks per round by skipping 3. (Incidentally, it's a good idea to desync your characters manually when attacking mages if they all happen to be synced, but this rarely occurs in practice.)
This isn't very noticeable for most characters because the engine animates them as if they were attacking at a constant rate, ignoring step 3. However, archers' attacks are actually animated correctly, which is why they appear to fire several arrows in relatively fast succession, then pause, then fire more, etc. This makes archers seems somewhat clunky and slow, but they actually attack faster than meleers (short bows get an extra 1 attack per round), it's just that the engine lies about the delay in melee attacks.
So, who needs a high speed factor? If you want to be able to interrupt mages, it's handy. Essentially all a good speed factor does is transfer the delay from step 1 to step 3. This decreases the average and minimum delay when you see a mage trying to cast and click on him, but if you start attacking right during part 3, you'll get the same delay no matter what your speed factor because the game will see that you've already attacked the maximum number of times and force you to wait until the next round. You can see this very well with archers: try switching targets right after step 2 and they'll delay quite a bit, but do so after step 3 and you'll see little delay at all.