A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are most often used to partition a two dimensional space by recursively subdividing it into four quadrants or regions.
Some common uses of quadtrees
Efficient collision detection in two dimensions
View frustum culling of terrain data
Storing sparse data, such as a formatting information for a spreadsheet or for some matrix calculations
Solution of multidimensional fields (computational fluid dynamics, electromagnetism)
Conway’s Game of Life simulation program.
Quadtrees are also used in the area of fractal image analysis