A bound morpheme is like a puzzle piece that only works when you put it together with another puzzle piece. It can't stand alone by itself. For example, the word "unhappiness" has two puzzle pieces, "un" and "ness," that join together to make the whole word. "Un" means "not," and "ness" means "the state of being."
Now imagine playing with Legos. If you have a blue Lego piece and a red Lego piece, they can't join together by themselves. But if you have a special connector piece that has bumps on both sides, you can snap the blue and red pieces onto it to make a bigger structure. The connector piece is like a bound morpheme because it needs both pieces to work together.
In English, many prefixes (like "un") and suffixes (like "ness") are bound morphemes because they only make sense when they are added to other words.