Defintion: DTE & DCE
DTE is acronym for Data Terminal Equipment.
Examples of DTE is computers, printers & terminals.
DCE is acronym for Data Communication Equipment.
Examples of DCE is modems.
Wiring a cable for DTE to DCE communication is easy. All wires goes straight from pin x to pin x.
But wiring a cable for DTE to DTE (nullmodem) or DCE to DCE requires that some wires are crossed. A signal should be wired from pin x to the opposite signal at the other end. With opposite signals means for example Transmit & Receive.