A constructed language or conlang is a language that is deliberately invented by one person (or occasionally by a small group). Conlangs are more or less like real-world, spoken languages (as opposed to, say, programming languages) but are often not based on any real-world language. The most famous examples are Esperanto, Klingon, and J.R.R. Tolkien's elvish languages, but there are zillions of lesser-known languages out there if you know where to look.
There are many reasons why you might want to invent a language. If you're interested in creating your own conlang, I'd advise studying a foreign language a little bit first, and then reading The Language Construction Kit by Zompist.