Top-down and bottom-up design are two ways of organizing a project or solving a problem.
Top-down design starts by looking at the big picture, then breaking it down into smaller and smaller parts. Think about it like building with LEGOs. When you start out, you have a lot of pieces, but you start by looking at the instructions and come up with a plan for how to put it all together. You know what you need to do overall, and then you start with the big pieces first, and then add the smaller pieces as you go along.
Bottom-up design also starts with pieces, but it starts with the small pieces first. For example, if you were building a treehouse, you might start by finding the right pieces of wood and then putting them together. Then you might add the roof, the walls, and all the other pieces until you have a complete treehouse.
In both top-down and bottom-up design, the goal is to take the pieces and put them together to solve the problem or complete the project.