A hash is a one way algorithm used to compare an input with a reference without compromising the reference.
It is commonly used in logins to compare passwords and you can also find it on your reciepe if you shop using credit-card. There you will find your credit-card-number with some numbers hidden, this way you can prove with high propability that your card was used to buy the stuff while someone searching through your garbage won't be able to find the number of your card.
A very naive and simple hash is "The first 3 letters of a string".
That means the hash of "abcdefg" will be "abc". This function can obviously not be reversed which is the entire purpose of a hash. However, note that "abcxyz" will have exactly the same hash, this is called a collision. So again: a hash only proves with a certain propability that the two compared values are the same.
Another very naive and simple hash is the 5-modulus of a number, here you will see that 6,11,16 etc.. will all have the same hash: 1.
Modern hash-algorithms are designed to keep the number of collisions as low as possible but they can never be completly avoided. A rule of thumb is: the longer your hash is, the less collisions it has.