A space-filling tree is like a puzzle made out of shapes that fit together perfectly. Think about how when you put together a puzzle, each piece has to fit exactly with the other pieces.
In the case of a space-filling tree, each shape is a "node" and each node is connected to other nodes by lines or pathways. These pathways create a sort of map that shows how all the nodes are connected.
The reason it's called a "space-filling" tree is because the pathways connect every node in the tree and fill up all the available space in the tree. It's kind of like when you color in all the spaces on a coloring book page - the whole page is filled with color.
These kinds of trees are used in computer science and mathematics to help solve problems and understand complex systems. By using a space-filling tree, scientists and mathematicians can see how all the parts fit together and work together to create a whole system.