Cell signalling is part of a complex system of communication that governs basic cellular activities and coordinates cell actions.
Cell signaling occurs by 2 methods, electrical and chemical signals.
Cells receive information from their environment, usually in the form of electrical and chemical signals. So Cell signaling is a way for a cell to receive information from it environment.
The cell has receptors on its plasma or cellular membrane that detects external signals and provides mechanisms for cell to cell communication. Membrane receptors allow cells to recognize, transmit, and respond to a variety of specific signals.
A technical definition I found is: Cell Signaling- all living cells sense and respond to their enviroment by a set of mechanisms known as cell signaling.