CW complexes are the basic building blocks of spaces. All, the basic concepts of Algebraic Topology can be understood and visualized via CW complexes. Homology, Cohomology, Cup Product are often easy to compute on these complexes, and a large number of qualifying/candidacy examination simply ask to compute these things on CW complexes.
One line slogan for constructing CW complex is
`Glue the boundary of n cell to n-1 cell
In the following two lectures I explain CW complexes and how they are built. You can go through the entire set of my videos on the YouTube channel.