Technically, the "UART" inside the 8051 is really a USART. Most people are familiar with the term "UART" so almost nobody uses "USART".

USART = Universal Synchronous/Asynchronous Receiver/Transmitter

The "Synchronous" part means that in Mode 0, the 8051 provides both data _and_ the clock signal. The data is sent or received on RXD pin and the clock is provided on TXD.

See the following screenshot from the Triscend FastChip software for a description.
http://www.8052.com/users/sknapp/uart_mode_0.gif

In the other "Asynchronous" modes, data is clocked internal the 8051. Transmit data is clocked out of the device on TXD at the baud rate. Receive data is sampled and resynchronized internally using some multiple of the clock frequency (the multiple depends on which 8051 variant).

In "Synchronous" mode, the 8051 provides the clock for both devices involved in the communication. In "Asynchronous" modes, there is no clock signal common to both devices. The 8051 resynchronizes the data to its internal clock.