Basically, it is during the years 1000-1400. Some people say it started as early as 476 when the Western Romans collapsed (The eastern side survived until the late 1400's).
Added to by John Ashtone. To add to the above answer, which is both correct and wrong at the same time?
It depends where in the world you are referring to.
Western Europe, it started in 406AD, when the Roman Legions were withdrawn from Briton. However most of the rest of Europe it was 476, with the collapse of the 'Western Roman Empire'.
1000 to 1400 is rather odd, but not totally inaccurate, there was a gradual collapse of writing and History, and these are some of the constituents to the 'Medieval period'.
"The Dark Ages", incidentally refer to when there is a lack of written History.
The Medieval period begins to end 1round 1400 with the advent of the 'Renaissance', however most Historians place the beginning of the end around 1453, with the fall of Constantinople.
In England the end of the Medieval period is often put at the arbitrary date of 1485, in fact you can be more precise and say around 6:00pm Monday, 22nd August 1485, which is when King Richard III was killed and Henry VII became King.
But the above is a joke, and it was really some time in the 16th Century, that the Medieval period in England became the Modern era.