Warning! Longer, more complex reply. RS232 was designed as the communication standard from Data Terminal Equipment (DTE - a 'terminal') to Data Communication Equipment (DCE - a 'modem'). The modem provides conversion to signals acceptable on the telephone line. At the other end would be another modem, connected via (presumably) another connection to a computer.
But people wanted to use the connection locally from computer directly to another computer. They could not be connected straight through pin-to-pin as the transmit on one computer would be directly connected to the transmit on the other computer. Other signals likewise would be connected to their identical counterparts and not to an appropriate pin. For example, handshaking signals RTS (Ready To Send) and CTS (Clear To Send) would either need to be cross connected or, in many cases, the RTS is simply locally connected to the CTS of the same unit.
Thus a 'null modem' cable provides the same effective connections as if a complete Computer-Modem-Telephone Line-Modem-Computer hookup existed. The minimal 'null modem' does indeed just cross Transmit and Recieve on one end to the appropriate opposite pin on the other. The 'modem control and handshaking' lines are dealt with in a variety of ways resulting in a number of designs for 'null modem' cables. One may not be right for all setups.