A hash function is a mathematical function: You enter data in the form of a string and get a shorter string of characters in the form of a hash.
Cryptographic hash functions are used for blockchains. These are so-called one-way functions and as such are difficult to reverse, i.e. one cannot deduce the input from the output. Furthermore, they are collision resistant, that is: As per todays knowledge it is impossible for two different input values to result in the same output value. As soon as even the smallest character within the input value is changed, the hash changes significantly.
Take the Blockchain: Each block has its own hash, so that the hash can be used for verification instead of the whole block content. For example, the Bitcoin block chain uses the SHA-256 hash function (SHA stands for "Secure Hash Algorithm"), which converts each input into a sequence of numbers and letters of exactly 256 bits, regardless of its length.