DTE

DTE is acronym for Data Terminal Equipment.

Examples of DTE is computers, printers & terminals.

DCE

DCE is acronym for Data Communication Equipment.

Examples of DCE is modems.

Wiring

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 I mean for example Transmit & Receive.