A dream is a series of sensory imputs and emotions involuntarily occurring in the mind during REM sleep.
AI's will sometimes have the ability to dream added to their programs. Noonien Soong added the ability to dream to Data. (TNG: "Birthright, Part I") The Doctor also added a daydreaming subroutine to his program. (VOY: "Tinker Tenor Doctor Spy")
In 2367 the crew of the USS Enterprise-D went slowly insane as they were unable to dream while trapped in a Tyken's Rift. (TNG: "Night Terrors")
In 2374 the USS Voyager encountered the dream species, a species of aliens that lived out their lives in dreams. (VOY: "Waking Moments")
Background
Although stated as such in TNG: "Night Terrors", REM sleep is not the exclusive purview of dreams - it is simply the most common time to dream. 5-10% of people who are woken during non-REM sleep also report dreaming. We can perhaps forgive Crusher being inexact as she was impaired by the effects of the Tyken's Rift.