Both "dinner" and "supper" can be used to describe an evening meal, and in that sense there is little difference between them.You would never serve supper at noon, but you might have dinner at midday -- although today it makes more sense to call that one lunch.
In earlier times, dinner was a heavy meal that farm laborers ate to sustain themselves through a long afternoon. Its use has changed with modern life, but it can still suggest a fuller evening meal, while supper can be lighter evening fare.
Grammar Girl
