The term Norman Conquest traditionally refers to the conquest of England by William, Duke of Normandy, subsequently King William I. William's victory at the Battle of Hastings in 1066 effectively completed the conquest, regarded as an important watershed, the start of "conventional" English history. (For the importance of the concept in mass culture, note the spoof history book 1066 and All That).
The Viking invasion of northern England by Harald III of Norway in September 1066 provided one factor aiding the ease of the Norman takeover - it left England unable to gather a large enough army to fend off the new enemy. Moreover, Norman cultural and political influence in England had built up over the years prior to 1066.
Note that the conquest of Wales by the Normans took place piecemeal and finished only in 1282, during the reign of King Edward I. The same king, though he subdued Scotland, did not truly conquer it, as it re-asserted local sovereignty, remained an independent kingdom until 1707 and retained a separate monarchy until 1603.
The Norman conquerors introduced Norman French as the language of the ruling classes in England, displacing Old English. Norman French retained the status of a prestige language for nearly 300 years.
At first the conquerors remained ethnically distinct from the native population of England but over the centuries the two groups merged and have become barely distinguishable.
Alan Ayckbourn wrote a series of plays entitled The Norman Conquests. Their subject matter has nothing to do with the Norman conquest of England.