I gave a long answer on the evolution of the English language a couple of months ago; you can find it here: https://www.reddit.com/r/AskHistorians/comments/cyq8dz/how_far_back_in_english_history_would_i_be_able/

u/bloodswan also gave a great answer that can also be found in the FAQ: https://www.reddit.com/r/AskHistorians/comments/6q37mx/when_i_hear_chaucer_spoken_in_middle_english_it/dkuj8bw/

Generally, languages evolve for a variety of reasons, the main one of which is: the population speaking it is alive, so the language is, too. Generally, language changes are introduced by certain social groups, and eventually, the rest of the population follows. You can see this very clearly with the huge influence of French on Middle English, as described in the first comment I quoted. If the entire upper class speaks French, you can imagine what an impact this has on the language as a whole. People take over a ton of loan words. The grammar changes, too. In u/bloodswan's comment, you can see that the higher classes played a clear part in the Great Vowel Shift, too.

Often, particular social groups wish to separate themselves from others (for instance, young people might speak in a way that's more 'fashionable'. In Dutch for instance a change is happening where instead of 'zij/ze' (they), younger people in certain regions/lower socioeconomic standing have started to use 'hun' (them), even when used as a subject. As you can imagine, this hurts the ears of grammar nazis and older people ;) This is a change that might peter out eventually, but as for now, it's going on strong, and older people started using it too. There's a fair chance that it'll be regular Dutch in 100 years time.)

Other people often want to be similar to the group that introduced the language change, and they start to mimic the changes. This often happens with higher socioeconomic groups, as you can imagine, but it also happens a lot with 'youth language'. So words can fall in and out of fashion - until the point where they are completely replaced. This happens with loan words for things that already existed in a language.

Also interesting: sometimes words become more specialised or more generalised. For instance the word 'fowl'. It comes from Old English 'fugel' (similar to Modern Dutch/German 'vogel') and it means 'bird'. However it got a more specialised meaning in English, namely 'birds for eating'. It's unclear where the word 'bird' came from, since it has no cognates in other Germanic languages, but it grew to have the same meaning as 'fugel' did in Old English. The original Old English word 'bridd' meant 'young bird/nestling', so as you can see, this meaning became more general!

Another factor of language change can be that people don't learn languages properly. This often happens when two languages come into contact with one another. As said, you can see this with (Middle) French and Middle English. The grammar of Middle English simplified a lot. This happens regularly when people take over another language or start mixing them: see pidgin languages as an extreme example. People also individually have slight differences between pronunciation: someone's 'sh' sound may be a tad closer to 'th', while another's might be a bit closer to 's'. Or they have a preference for a particular word or rhythm in their speech. Small differences could result in big changes, depending on who speaks that way and how much they influence others.

There's a ton more to say about this, but I couldn't find my books on psycholinguistics quickly enough, so this is it for now. Sources: 'A history of English: a sociolinguistic approach' by Barbara A. Fennell, and 'Taal en taalwetenschap' by René Appel, Anne Baker, et. al.