It's called a trackpoint button. I've got one on my ThinkPad T410, and I like it. Some people don't, and it can be disabled. Once you get the hang of it, it's much faster than using the pad to move the pointer -- not just from a human factors aspect, it is actually accelerated. Push it down harder and the pointer moves faster.
It also has a "magnifying glass" function -- helpful when I can't quite tell if I have a period on the screen or a comma.
http://support.lenovo.com/en/documents/ht000611
There are also Youtube videos on its use.