The newer generation cameras all come with x number of AF points, and Y number of these points are cross type sensors. hhhmm..Cross type? Remenicent of the Counter Strike era.. yeah just walk in front of my cross type and I'll … ok fine.. not relevant.. good old days..
Anyway I found an article that discusses about this here.
Basically in a nutshell, AF sensors work by detecting the contrast of a scene (Passive AF). The usual single type sensors are all verticle sensors which allow the camera to determine along that verticle line, which part is in focus. Everything is all well and great when you have contrasty subjects that has a certain height. But for subjects that are moving from side to side? not so good.. this is where the cross-type sensor comes in.
This type of sensor checks for both horizontal and vertical contrast, allowing the photographer to obtain lock on difficult (fast or dimly lit) subjects more frequent. If not you'll get those AF hunts that isn't as fun as it sounds.
The faster the lens aka bigger the aperture, allows the camera to use all of its focusing points. So a lens with a f/2.8 will focus better when compared to a f/3.5 – 5.6 lens. Using this lens, at the zoomed end, the max aperture is only f/5.6 which will greatly reduce the number of focusing sensors, some cameras drop the total sensor count to just the one in the middle.
So not only a f/2.8 lens is bigger, brighter, faster but also gives the camera better AF capabilities hence the word 'fast' being associated with lenses with a lower f-stop.