It's not a game, but an astronomy tool for the PSP generation. The view of the heavens depends on the position of the observer on the Earth. This can be set manually, or automatically by the PSP GPS unit (sold separately at almost three times the price of the software). Up/down and left/right on the D-pad control the altitude and azimuth respectively, allowing the player to change the section of sky they are viewing. The shoulder buttons zoom in and out of the star field, and the analog nub can be used to get more information about particular objects. There are numerous options, including changing the threshold for the stars that are visible, adjusting the rate at which time passes and the position of the viewer on the Earth. Some novelties have been thrown in as well, like the night sky on Easter Island the day the Moai statues were discovered, what the sky was like during the last ice age, etc. Novel but not particularly useful - the Easter Island one is basically the sky with some Moai statues on the land.
One big drawback to it is the brightness of the PSP screen when actually trying to use it in the field. After the observer's eyes have gotten accustomed to the darkness outside the shine of the console means another few minutes before they can get darkness-adjusted again. Astronomy software like Google Skymap commonly feature nightmodes, where the whole image is tinted red (red being the darkest of visible light and barely affects eyes that are already darkness-adjusted). Sadly this is not a feature of Homestar Portable. This shows how it is more of an in-door application, which is a shame considering the ease of use and portability of the PSP compared to a laptop or netbook.
Aside from the sky view mode there is also the fantasy theatre mode, where various aspects of the night sky are described by commentary (in Japanese) and accompanied by panning and zooming visuals. This feature would be more suited to a device with a larger screen that could be enjoyed by all the family. The TV output of the PSP goes someway towards this but just isn't enough.
Overall, Homestar Portable tries to be too much and should have been focused in one direction. As an astronomy tool it's a little overpriced, and as family entertainment it's limited by the hardware it's been released on.