Asynchronous and synchronous are two ways different of encoding bytes of data into electrical signals on a serial cable.
Some (most?) serial ports on routers can handle only synchronous encoding of the data. Some serial ports, e.g. the AUX port of a router, can handle only asynchronously encoded data. Some serial ports, e.g. in a 2509 router, or an NM-8A/S, can handle either format, and can be switched between the two with a configuration command.
Asynchronous encodes each byte of data separately - each byte has a start bit and an end bit, and there os no timing relationship between one byte and the next. Synchronous encodes a whole block of bytes as a single frame.
Hope that helps clear up the confusion.
Kevin Dorrell
Luxembourg