It is not that complicated, to make a simple example with strings: AAAABBBABABAB takes up 13 spaces, but write (compress) it like 4A3B3AB take up 6 spaces compressing it more than 50%.

Now double it like AAAABBBABABABAAAABBBABABAB with 26 spaces and write it as 2(4A3B3AB) with 9 spaces it takes only 30% of the space.

Compression algorithms just look for those repetitive spaces.

Takes those letters and imagine them being colored pixels of a picture to compress a picture