A CW complex is a type of topological space that is constructed by gluing together basic building blocks called cells. These cells can be thought of as simple shapes, like points, lines, and disks, which are attached to each other in a specific way. The construction process involves starting with a set of points (0-cells) and then adding higher-dimensional cells (1-cells, 2-cells, etc.) by attaching them along their boundaries. The key feature of a CW complex is that it allows for a flexible way to study topological properties. By using cells, mathematicians can analyze complex shapes and spaces in a manageable way. This makes CW complexes a fundamental tool in algebraic topology, where they help in understanding the structure and classification of topological spaces.