Multiplexing allows you to drive a large number of display elements with fewer wires than individual addressing, at the expense of a more complex control algorithm. The part in question is a common anode display, but common cathode displays are just as common. This arrangement and control method is called multiplexing, and the linked article will give you a lot of information. The controller enables one of the common anodes, drives the segments, and waits, then turns off the cathodes and moves on to the next common anode. Each digit has its anodes connected together, and the segments for all digits have their cathodes connected. Actually this is a very common arrangement.
