If we are talking about functions that are reversible (as opposed to those that are not like hash functions), then the main idea of a one way function is that its easy to compute, but hard to invert.
In a function that is invertible, you have an inverse map which is f^(-1)(x) where you can use f^(-1)(f(x)) = x to get back your original input. This is what happens in cryptography where you encode something by using h = f(x) and then you apply f^(-1)(h) = x to get back your original data.
If it is hard to undo (or invert) it means that the computational complexity for undoing is going to be high (like exponentially high or greater than polynomial).
The class of problems that are hard to compute or find but easy to check are called NP problems. You can check the solution very quickly, but finding the solution probabilistically will take a long time.