An error message is a piece of text intentionally displayed by a piece of software to indicate when there is a problem of some kind. It may be displayed on a screen or added to a log file of some kind.
An error message is often a critical piece of information to have when trying to diagnose and fix a problem. Searching the internet for a particular error message will frequently yield posts by others who have run into the same problem, sometimes including a solution (though the same error message may require different solutions under different circumstance). Even if the solution is not spelled out, however, having additional information often points towards a solution or at least helps to narrow the field of investigation.