That part in itself converts single-ended transmit and receive signals to a differential, higher current bidirectional signal. This is part of the RS485 spec (and others) to improve the effective distance the signal can be sent, and reduce the number of pairs.
What this part does not implement is the serial conversion itself. This requires some form of shift register, so that (e.g.) an 8-bit value can be sent over a single line or pair, by presenting one bit on that line or pair at a time in a predetermined order. Also included are synchronization mechanisms so that the receiver always knows which bit is being sent at any particular time. The receiver shift register--again, on a different part, probably a uC--then collects them and presents them as a complete byte to the processor.