Multiplexing is a name for any system which allows multiple signals to be mixed and seperated. Specifically, a system in which signals pass between two units in both directions is known as a duplex system.
The simplest multiplexing, perhaps, is time multiplexing (also called time-division multplexing). The same medium is used for all signals, but signals may only go in one direction at any particular time. Time-division duplex is known as half-duplex, while all other types of duplex are known as full-duplex.
Regular time multiplexing would be like a system with a 3-second period, one second being allocated to signals from unit A, one second being allocated to signals from unit B, and one second being allocated to signals from unit C. If unit A has a message to transmit (to either B or C), it must wait for it's allocated time (the maximum waiting time, then, would be 2 seconds). Of course, during the two seconds that unit A is not allowed to transmit, it must still monitor the bus for messages from one of the other units, in case there is a message that e.g. unit C needs to send to unit A. One problem with this kind of time-multiplexing is that all units must be synchronized all the time in order to agree not to use the medium at the same time. At least some digital cellular phone systems use regular time multiplexing.
Irregular time multiplexing is used, for example, on the I2C bus. A master may wish to transmit a command to one of several slaves, and receive a response from that slave. When the bus is idle, the bus is allocated to signals from the master. When the master transmits a command to a slave that requires an acknowledge or a response, the bus will be allocated to signals from that slave once the command is complete. The bus remains allocated to the slave until some event: the slave's response is complete, or the slave asks for an acknowledge or for more data from the master. (A timeout may also be used in an irregular time multiplexing system, but timeouts are not used in I2C.) Again, all units must agree not to use the medium at the same time - in this case, it is accomplished by monitoring bus traffic for commands, rather than by keeping track of time. (The I2C protocol is even more complex than this, with provisions for many masters on one bus. One of the things which allows for this is that signals may actually be sent simultaneously by more than one unit, because all outputs are open drain, and there are pull-up resistors on the bus lines. If, at any time the bus is allocated to masters, any master detects a signal on that line that it is not transmitting, it must concede arbitration, i.e. give up control of the bus to whatever master was sending the signal.)
Frequency-division multiplexing is how radio stations may all transmit their own signals continuously without interfering with each other. The medium must have a large bandwidth in order for this multiplexing to work. Many signals may be sent at the same time, all at different frequencies. The signals are seperated with filters.
Medium-division multiplexing is a name for a system with a different medium for different signals. An RS-232 bus uses medium-division - there is one wire carrying data signals from the DTE, there is a different wire carrying data signals from the DCE.
Note that multiplexing methods may be combined. For example, a medium may be frequency-multiplexed into two 'channels' X and Y. Channel X itself may be regularly time-multiplexed. Channel Y may be irregularly time-multiplexed.