The Church-Turing thesis basically says that a Turing machine
can be taken as the definition of computation: if a
Turing machine can do it, it's computable; otherwise, it's
not. Any theoretical computational model, real-world
computing device or programming language that can simulate a
Turing machine is, therefore, as powerful as a computer can be
--- though some are faster, and some are slower.
We call such computational devices or programs Turing
complete.
Perhaps you've heard people say that HTML is not really a
programming language. We can now make that precise: HTML is
not Turing complete. You cannot simulate a Turing machine
in HTML.
If you're with some computer nerds and one starts spouting
off that language X is so much more powerful than language
Y, you can shut him up by saying: "They're both Turing
complete, so neither is more powerful than the other."