Language changes because of people's exposure to other languages. English, for example, has added words from all over the world. This goes back to the various conquering of the British Isles, by the Scandinavians, by the Romans, and by the Normans. And we have been adding words from other languages ever since.
Languages change because people move. When they do so, they experience new experiences, see new flora and fauna, and the longer they are away from their original people, the more the language tends to change.
Language changes because of science and technology. We need new words to describe the things we discover and invent. Hebrew is a good example, an ancient language used only for religious ritual until the founding of the state of Israel. There were no coffeemakers or computers in the Bible.
Language changes because of youth. Young people want to express themselves in their own "language," a way of being separate from the older generation, which is what much slang is for. Eventually, some of this slang enters the mainstream language, at which point our youth have to invent new slang.
Language changes because of politics. The terms used in the political arena frame issues in ways that are meant to poison the well. New terms and expressions arise, some quite interesting, some quite distasteful, but we have gone from "atom bombs" to weapons of mass destruction. Orwell commented on this in a rather famous essay in 1946. I have included a link to the essay below.
There are other reasons, some having to do with "drift" in consonants and our general tendency to laziness, always looking for an easier and faster way to say something. Sometimes new words are simply erroneously heard, for example the word "nickname," which experts have theorized comes from the term "an eke name," a combination of words which kind of slid together over time. Sometimes words change completely in meaning, such as the word "awful," which used to mean "full of awe." This is likely to have happened because something terrible can fill one with awe. There are other reasons, which have filled books, but I hope this is a good start.