The event that began the transition from Old English to Middle English was the Norman Conquest of 1066, when William the Conqueror (Duke of Normandy and, later, William I of England) invaded the island of Britain from his home base in northern France, and settled in his new acquisition along with his nobles and court. William crushed the opposition with a brutal hand and deprived the Anglo-Saxon earls of their property, distributing it to Normans (and some English) who supported him.
The conquering Normans were themselves descended from Vikings who had settled in northern France about 200 years before (the very word Norman comes originally from Norseman). However, they had completely abandoned their Old Norse language and wholeheartedly adopted French (which is a so-called Romance language, derived originally from the Latin, not Germanic, branch of Indo-European), to the extent that not a single Norse word survived in Normandy.
However, the Normans spoke a rural dialect of French with considerable Germanic influences, usually called Anglo-Norman or Norman French, which was quite different from the standard French of Paris of the period, which is known as Francien. The differences between these dialects became even more marked after the Norman invasion of Britain, particularly after King John and England lost the French part of Normandy to the King of France in 1204 and England became even more isolated from continental Europe.
Anglo-Norman French became the language of the kings and nobility of England for more than 300 years (Henry IV, who came to the English throne in 1399, was the first monarch since before the Conquest to have English as his mother tongue). While Anglo-Norman was the verbal language of the court, administration and culture, though, Latin was mostly used for written language, especially by the Church and in official records. For example, the “Domesday Book”, in which William the Conqueror took stock of his new kingdom, was written in Latin to emphasize its legal authority.
However, the peasantry and lower classes (the vast majority of the population, an estimated 95%) continued to speak English - considered by the Normans a low-class, vulgar tongue - and the two languages developed in parallel, only gradually merging as Normans and Anglo-Saxons began to intermarry. It is this mixture of Old English and Anglo-Norman that is usually referred to as Middle English.