The Comet Obervatory is the main hub of Super Mario Galaxy. From here you may access the many galaxies in the game using domes. It is also where Rosalina and her Lumas live. It is first accessed through Gateway Galaxy. A new dome is opened every time you collect a Grand Star (with the exception of beating The Center of the Universe level). Once five Grand Stars are collected and you have 60 or more stars in total, you may travel to the Center of the Universe to save Princess Peach.
There are six domes in the Comet Observatory. They are unlocked in the following order:
Unlocked alongside the Garden is Gateway Galaxy, which can be accessed through the house on the small planetoid across from the Garden. Also, each dome has its own Hungry Luma, which will unlock one additional galaxy for each dome if you feed it.
Outside of Super Mario Galaxy, it has made appearances in