A "hashing function" is a mathematical algorithm that converts an input string into some other form, often for ease of lookup. The most important element of password security for hashing functions is that they are one way, that is, you can't get the original string back out of the hashed value.
When you input your password, it is hashed and checked against a table that stores the hashed value of your password, and are allowed access if they match. But the hashed value can't be used to reconstruct your password.