'dolphin divers' is a phrase used by fps gameplayers to describe a certain combination of moves, normally as follows
1) running
2) go prone
3) select 'iron' sights on rifle/weapon
4) fire
5) run
So, as you can see there are at least 5 buttons to press to get this effect, more if you fire more than once.
My fingers are fast but you must realise it takes time to do the sequence. But,,, it is possible with some gaming mice and keyboards to make a 'macro' to combine all the actions above into one button press, obviously this is much quicker than my fingers. Result more kills, less risk.
Why prone? Most fps games will give you a higher damage shot whilst prone, ie more accurate.
Why Ironsights? More accurate especially over a distance.
When you see it used in action in a game, it looks just like someone running at full speed, diving to the ground taking 2 or 3 shots then up and running again all in about 1 second.
In BFBC Beta I quoted above proning has not been coded in to the game so you cannot 'dolphin dive' in the game only walk, run or crouch.