What is a hash in Bitcoin?
The fingerprint of some data: a fixed-length output of the SHA-256 function, which Bitcoin uses for addresses, transaction IDs and mining.
A hash function turns any data into a short, fixed-length code. Change one character of the input and the code comes out completely different, yet the same input always gives the same code — that's why it works as a fingerprint.
Bitcoin uses one called SHA-256 throughout: transaction IDs are hashes of the payment, addresses carry hashes of keys or scripts, and mining is the search for a block hash below a target. Working backwards from a hash to its input is not practically possible.