What a hash is and why it is one-way
A hash function turns any input, a word, a password, a whole file, into a fixed-length string of characters called a digest. The same input always produces the same hash, but the process is one-way: you cannot reverse a hash back into the original. Even a tiny change to the input produces a completely different hash, which is what makes hashing useful for checking integrity.
The common algorithms. MD5 and SHA-1 are old and now considered broken for security because collisions (two inputs sharing a hash) can be engineered, so they survive only for non-security checksums. SHA-256 is the modern standard for integrity. For storing passwords, plain hashing is not enough; purpose-built, deliberately slow functions like bcrypt or Argon2 with a unique salt are used to resist brute-force attacks.
What it is actually for. Two main jobs: verifying that a downloaded file was not corrupted or tampered with (compare its hash to the published one), and storing passwords so that even a breached database does not reveal them. The tool above generates common hashes from any text so you can check a file or see how the algorithms differ.