Question

What is one possible message that one cell might send to another cell

Answer 1

that really just depends on what type of cells we are talking about here. :) Bacterial cells can send a huge array of signals, like in pathogenic bacteria at the time of colonization, they send out signals to neighboring cells in the form of chemical substances to produce virulence factors like toxins. In short, gene regulation changes are brought about. This is just one example and is one of the effects of a process called Quorum Sensing. 

Answer 2

Cells can sense and respond to electromagnetic signals, such as light, and to mechanical signals, such as touch. However, cells most often communicate with each other using chemical signals.