My favorite analogy stems from my sophomore year in high school. They were adding a wing onto the building, and one wall, and all the lockers on that wall, had been demolished. This left us with fewer lockers than there were students. Some students had to share a locker.
Two students, who share a locker, have their geometry books in that locker. One of them needs a geometry book, and grabs one from the locker. She might get her own, or she might get her locker mate’s.
Floating point numbers have 53 binary significant figures. In some ranges of numbers, there are more 16 digit decimal numbers than there are 53 digit binaries. Some of those decimals need to share a binary locker. The result you get out, may be the number you want, or it might be its locker mate.