Hashing algorithms are usually cryptographic in nature, but the principal difference is that encryption is reversible through decryption, and hashing is not.
An encryption function typically takes input and produces encrypted output that is the same, or slightly larger size.
A hashing function takes input and produces a typically smaller output, typically of a fixed size as well.
While it isn't possible to take a hashed result and "dehash" it to get back the original input, you can typically brute-force your way to something that produces the same hash.
In other words, if a authentication scheme takes a password, hashes it, and compares it to a hashed version of the requires password, it might not be required that you actually know the original password, only its hash, and you can brute-force your way to something that will match, even if it's a different password.
Hashing functions are typically created to minimize the chance of collisions and make it hard to just calculate something that will produce the same hash as something else.