A little bit of history: developed in 1928 and commercialized in 1933 it was hailed as a shatter proof replacement for silica glass. It was first branded as Plexiglas by the Rohm and Haas Company and has since been sold under names such as Lucite and Perspex. Its chemical structure is shown below.
Why is PMMA so cool? Well, it can be easily cast to make basically any shape you want. And its clear, and you can add dyes to make sweet translucent objects, and you can embed stuff in in (kind of like how amber embeds bugs).