Super Mario Galaxy is a portal into a universe where the most common call-out for plumbers is "there are turtles in my drains", but unfortunately the only competent plumber is stuck far away from home in a starship-cum-house wiling away his days collecting stars, coins, and Ricicles in a desperate effort to gain some respect from Princess Peach who always treats you like her personal slave and expects you to rescue her every time she gets kidnapped, which is a hobby of hers.
Its plot is about as interesting as Sunshine's was before it, except you're in space. Thankfully, due to laws of physics known only to Italian plumbers from Japan venturing out into space without a space suit does not kill Mario.
The game also succeeds in belaying any thoughts you may have had about galaxies being formed over millions of gajillions of years. They are actually formed in seconds by little star-like people when they TRANSFOOOOOORM. The game's title is actually a misnomer, as there are many galaxies in the game, not just one. This we can accept as a translation issue due to Japanese having no grammatical plural. Oddly, most galaxies reside in rooms of the house, such as the bedroom and the kitchen.
The main enemy in the game are small white rabbits, which you must collect enough of to make some kind of soup that gives you super-human powers (or maybe it's just to create more clones of yourself).
Thankfully collecting the usual power stars is interrupted by the odd interlude where you must defeat a boss about as terrifying as Barney (and possessing a similar IQ).
This may sound like a daunting game where death awaits at every corner (and it is), so you'll be happy to know that your brother Luigi helps you on your quest by travelling to galaxies, finding a star, and then getting stuck, having to send you a letter with a photograph showing you exactly where he is cowering. He apparently has not worked out how to use stars to escape galaxies and return to the starship at the centre of the universe unlike his overachieving older brother.
A new discovery in plumber-physics is the ability of Mario to change into anything ... as long as it ends with "Mario". Such as Bee Mario, Boo Mario, Spring Mario, Ice Mario, Fire Mario, and finally Flying Mario (which tries to be clever and use another lexical category for the X in X Mario). Note that Mario cannot transform into a marionette. This is because marionette only starts with Mario, it does not end with Mario.