A wreath product is when you take one set of things (let's say apples) and another set of things (let's say oranges) and kind of match them up in a special way. It's like making a big circle (like a wreath) with the apples on one side and the oranges on the other side.
Here's an example: Let's say you have 2 shirts you really like – a blue one and a red one – and you also have 3 pairs of pants you really like – black, blue, and grey. With a wreath product, you would match up each shirt with each pair of pants. So, you would wear the blue shirt with black pants, then with blue pants, then with grey pants. Then you would do the same thing with the red shirt – wear it with black pants, blue pants, and grey pants. That's what a wreath product is – matching up different things to create a kind of circle or loop.