With serial communications, bits are sent/received 1 bit at a time and each bit is sent/received at a specific time interval. Baud rate, as mentioned above, is just the measure of how many bits can be sent/received in 1 second. This determines the period of each bit (i.e. the time interval between each bit being sent/received) and the period is equal to 1/Baud. Example, a baud rate of 9600 would have a period of 1 / 9600 = 104.1uS (microseconds). This means that 1 bit is being sent/received every 104.1uS.
With asynchronous serial communications, each serial device times the bits via its own internal bit timer (no external clock signal provided). The baud rates at both the tx and rx ends must be pre-agreed upon and the two must match. If they do not match, you will either get framing errors or the received byte will not match the byte that was transmitted.
With synchronous serial, you have a master device and one or more slave devices, and an external bit clock signal that is generated by the master device. Both can transmit and receive, but only the master can generate the external clock signal. With I2C, you can have one or more master devices with just two wires. One for bi-directional data and one for the serial clock. Again, only the master can generate the external bit clock signal.