While I've never actually implemented the behavior described above, I did happen to do a bit of Google'ing (more on that below).
I want to know how to paginate like linkedin and facebook so it will list more rows when the user scrolls down?
also, What do you call this type of pagination?
I suspect I'd still just call it "pagination." That's all it is, in the end; you're navigating through small chunks of an entire result set. The only difference is how you do the navigation; rather than a "Next" button and/or a hyperlinked list of pages, it's the user's scrolling to a certain point on the page that triggers the same action as clicking a "Next" button.
The brief bit of Google'ing I did turned up two possible methods to achieve this scrolling behavior:
Something akin to jQuery Waypoints
Using your own custom "onscroll" event to estimate when the scrolled position is near the "bottom" of the page (seemed error-prone and/or harder to make cross-platform compatible).