The Battle of Hastings is highly regarded as one of the most important events in history, but how is it that this one battle affected English so drastically? And how have other similar battles not changed and altered languages the same?
Prior to the Battle of Hastings 1066, English (or Old English/OE, as it is known), was a Germanic language, similar to Old German, since the Germanic tribes of Angles, Saxons, Frisians and Jutes had migrated to England a few centuries earlier. To give you some idea: a German native speaker nowadays can still recognize and understand substantial amounts of an OE text, while a native English speaker might not.
Anyway, in 1066, William the Conquerer won the Battle of Hastings and conquered England (hence the name). He came from Normandy in France, and the Normans spoke a certain type of French. When he established his rule in England, the upper/ruling class consisted of Normans and England became kind of tri-lingual:
A good example of this is the use of word pairs like pig & pork. The lower classes, let's call them the English people, were farmers who had pigs (pig is a Germanic word). They didn't eat the meat themselves, however. The Norman/French upper class ate it and used the French word pork. The same goes for cow/beef, sheep/mutton, etc.
Gradually, this linguistic divide lessened and many French words were integrated into English (what was then Middle English, or ME), and eventually even the nobility began speaking English again. Towards the end of the 15th century, the ME period ended when English gradually became standardised (there had been many different dialects up to this point). An important factor in this was the first English printing press (William Caxton).
Even though English grammar also changed (and was simplified) during the ME period, the influence of French is mainly in terms of lexical inventory/vocabulary - something almost everybod would understand and notice.
The linguistic importance of the battle thus comes from the fact that the invaders spoke a different (you could also say an entirely different) language and their reign lasted long enough for both languages to merge. Another factor is that almost the entire English noblity was either killed in the battle or executed as traitors afterwards, which made it even easier for the Normans to asser French as the language of Government.
If you want to read more about this, your best guess is books from the field of linguistics, such as:
Let me know if you have any more questions.
Some interesting class stuff from the invasion is still in English.
Most barnyard animal names are more closely tied to old English (the language still spoke by the peasants) Example (Cow, Pig (swine), Sheep, and Deer (though not a barnyard animal it fits). But, when you eat the animal its name changes to a frankified word. Respectively (Beef, Pork, Mouton, and Venison).