The Hina Matsuri [雛祭り] is a festival that takes place on the 3rd of March to wish the healthy and prosperous growth of young girls (like Mirai-chan). During this time, ornamental dolls called Hina Ningyo [雛人形] are displayed on tiered steps which are covered in red cloth.
Here is our Mirai dressed up as the Empress who sits with the Emperor on the top tier of steps.
The second tier displays court ladies and the third tier displays musicians. Not all Hina platforms are displayed like this however and can just be filled with a load of dolls on each tier.
The Hina Matsuri tradition started during the Heian period in Kyoto where daughters of noble families would play with the dolls. It wasn't until the Edo period however when the tradition really started to take off across Japan with folks displaying the Hina dolls on the steps covered in red cloth.
Traditionally, Hina dolls are said to absorb evil spirits in place of your real 3D daughter. As the Hina dolls contain evil spirits, they shouldn't be kept around for too long as your real daughter would not be able to get married happily. Thus the Hina dolls should be put away soon after the Hina Matsuri.
During the Heian period, Hina dolls made out of paper were set afloat on a river which would later be collected and burned.