Programming language is an artificial language created so that humans can relatively easily communicate algorithms to computers. Such language often tries to mimic human language (practically always English) but is much MUCH simpler so that a computer can actually analyze it and understand it precisely so it also partially looks like math expressions. A programming language can be seen as a middle ground between pure machine code (very hard to handle by humans) and natural language (very hard to handle by computers).
For beginners: a programming language is actually much easier to learn than a foreign language, it will typically have fewer than 100 "words" to learn (out of which you'll mostly use like 10) and once you know one programming language, learning another becomes a breeze because they're all (usually) pretty similar in basic concepts. The hard part may be learning some of the concepts.
A programming language is distinct from a general computer language by its purpose to express algorithms and be used for creation of programs. There are computer languages that are NOT programming languages (at least in the narrower sense), such as HTML, json and so on.
We divide programming languages into different groups. Perhaps the most common divisions is to two groups:
Sometimes the distinction here may not be completely clear, for example Python is normally considered an interpreted language but it can also be compiled into bytecode and even native code. Java is considered more of a compiled language but it doesn't compile to native code (it compiles to bytecode). C is traditionally a compiled language but there also exist C interpreters etc.
We can divide language in many more ways, for example based on their paradigm (impertaive, declarative, object-oriented, functional, logical, ...), purpose (general purpose, special purpose), computational power (turing complete or weaker), level of abstraction (high, low), typing (strong, weak, dynamic, static) or function evaluation (strict, lazy).
{ THIS IS NOT A COMPREHENSIVE LIST, I can only include languages that I am familiar with, please add more ~drummyfish }
All content available under CC0 1.0 (public domain). Send comments and corrections to drummyfish at disroot dot org.