The physical act of pulling a chair over to a table of some sort, and sitting down in said chair at said table. In yet another stunning display of forethought, the English language has once again misrepresented something: to pull something up implies that 1. you are above that thing, and 2. that it moves in an upward direction. When you "pull up a chair", niether of these conditions are met.
This is also a phrase that carries pretty much the same meaning as "come join us", used often by a group inviting someone they know to join in the food, conversation, game, or whatever. Variations include "pull up a patch of carpet" or "pull up a piece of floor" when the group is chairless.