Theory

A set of ideas that explain something.

In Mathematics a theory is the set of theorems and principles that make up a branch of mathematics, such as Number Theory, Set Theory, etc.

In Science a theory is well understood, has been properly examined, and can be tested again and again and always works, such as the Theory of Gravity.

But in everyday language a theory is an explanation that may be true but has not been properly tested. So be careful about this confusing difference!