system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Turing completeness

What is meant by this term?
gpt
It basically means that a computer, or a computer language, is as powerful as a Turing machine. Powerful in the sense that it is possible to solve all the problems that a Turing machine can solve. It doesn't say anything about how fast it would solve them or how easy it would be to make the programs that solve the problems, just that it's possible to solve them.

A Turing machine then is a simple mathematical model of a computer. It's not a real machine or anything that's meant to be built really, though some people have. It's just a model of what computers do without all the fluff that doesn't really concern the mathematical nature of computing.

Then there's something called the Church-Turing thesis which states that a Turing machine is as powerful as any computer can be. So if something, being Turing complete, is as powerful as a Turing machine then it's as powerful as anything can be. 

Church-Turing thesis hasn't formally been proven. It's a bit hand wavey in the first place. You'd have to define some exact boundaries of what kind of computers you consider if you wanted to formally prove it, which would then probably make the whole thing a bit trivial. However, several other models of computation, that model computation in quite different ways than a Turing machine, have been proven to be exactly as powerful as a Turing machine. So that's led people to believe that maybe that's the best any model of computation can ever do.