Ok kiddo, have you ever played with building blocks? Imagine you have a few blocks of different shapes and sizes, but they all fit together nicely to make a tower.
Now imagine you have a bigger block that's made up of many smaller blocks - like a jigsaw puzzle. This bigger block is a "derived" block, because it's made up of smaller pieces.
In math, we have something called a scheme which is a mathematical object that helps us study shapes and patterns. Just like building blocks, we can make a bigger scheme by putting smaller schemes together.
A "derived scheme" is a way for mathematicians to take many smaller schemes and put them together to make a bigger, more complicated one. We do this so that we can understand these complicated schemes better - just like how we can understand the big block better by looking at all the little blocks that make it up.
So just like building blocks or a jigsaw puzzle, we use derived schemes to help us study shapes in math!