Were the Terracotta Figures and Horses buried on purpose? Why do we find them buuried?

You are correct that the Terracotta Figures and Horses were buried on purpose. Actually, the magnificent site was constructed by Emperor Qin Shihuang as his underground imperial army after his death. So when the figures and horses were found out, they were all buried.

They thought this army should be buried with the owner of it so they buried it.