The Cathedral was built in the mid-16th century on the orders of Ivan the Terrible to commemorate his military successes. The original building contained eight side churches (not chapels) arranged around the ninth, central Church of Intercession (he had lots of victories!). As if that was not enough a 10th church was subsequently added to the group over the grave of St Basil himself.
The building's unique shape supposedly represents a flame of a bonfire rising into the sky.
Legend has it that Ivan the Terrible blinded the architect so that he could not re-create such a beautiful masterpiece again. This is unlikely as apparently the architect (Postnik Yakovlev) was still working well after the Tsar's death in 1584.
The photos on this page show mostly the iconostases of some of the churches. I am not sure which are original (surviving the communist atheist purges) and which have been recreated. Whichever, they are very colourful and distinctive.