There are two related types of functions that are not themselves encryption functions, but are very important to many cryptographic algorithms and protocols. These are one-way functions and cryptographic hashes.

One-way functions: It is believed there are many functions that are computationally easy to compute, but computationally infeasible to reverse. In the physical world, we notice that it is a lot harder to get the toothpaste back in the tube than it was to get it out. Or a lot easier to burn a sheet of paper than it is to re-create it from smoke and ashes. Similarly, it seems a lot easier to multiply together some large primes than it is to factor the product. The scandalous fact, however, is that there is no rigorous mathematical proof that any one-way functions are really as hard to reverse as we believe they are. Still, cryptographic one-way functions are ones that we know how to perform in milliseconds on computers, but believe it would take these same computers millions of years to reverse (given only the result, of course, without cheating by looking at the original input).