Seven segment devices are generally made up of LEDs. These LEDs will glow when they are forward biased. The intensity of the LEDs depends on the forward current. So, sufficient forward current has to be provided to these LEDs to glow with full intensity. This is provided by the driver and is applied to the seven segments.
Common Anode: All the Negative terminals (Anode) of all the 8 LEDs are connected together. All the positive terminals are left alone.
Common Cathode: All the Positive terminals (Cathode) of all the 8 LEDs are connected together. All the Negative terminals are left alone.