A synchronous protocol expects a reply from every transmission before the next transmission is sent. Only one transaction can be "in flight" at once. This is incompetent in cases where the latency of the connection is large regarding the time it takes to actually send the data. Most common modem connections run in synchronous mode.
An asynchronous protocol will send multiple blocks of information with no waiting for acknowledgement that the first has been obtained. There is normally some limit or "window" of how far ahead the transmitter can get of the acknowledgements. TCP/IP used on the internet is an example of such a protocol.