A cryptographic "hash" creates a unique signature for a message. The key feature behind a hash is that it is "one-way". That means that while you can generate a hash from plain-text, you could never create plain-text from a hash. For example, let's say that you create a story that is 20 pages long, and you want to make sure that nobody alters to the story. You run one of hash algorithms over the story creating a 128-bit hash. In theory, it is virtually impossible to create another version of the story that matches that same 128 bit value.
Hashes are a "cryptographically secure" form of a "checksum" or "CRC". A checksum is used to detect unintentional changes in data, such as when a network packet gets corrupted when transmitted over a wire. A cryptographically secure hash, on the other hand, is used to protect data from intentional changes in data.
