Remember that initial microbial stage of Spore? You're a little dude swimming around, eating up other little dudes to increase your size and evolve to the next stage of development. Remember flOw, and Osmos? They were basically the same thing. Solar 2, for the most part, is identical to these concepts, except where Spore and flOw and Osmos drop you down to microscopic scale, Solar 2 does the polar opposite and puts you space. Similarly, as you advance in the aforementioned games, you get larger and more powerful. The same happens in Solar 2, except just on an increasingly more ridiculous scale.
In Solar 2, you start out as an asteroid, flying along in the void, with seemingly nothing to do, until you accidentally hit another asteroid and absorb it's mass. "Oh!" you think to yourself, "I see now.", and so begins your reckless tumbling through the universe on a quest to absorb as much mass as possible.
When you finally hit that threshold, you suddenly find yourself as a planet. Planets have serious gravity about them, and as you fly through the myriad asteroid fields you encounter, your planet will start capturing asteroids in its gravity well, and you'll absorb a whole *bunch* of mass, en mass. See what I did there?
Eventually your planet will absorb so much mass that it'll become habitable to life, which will efficiently skip over the niggling little aspects of evolution that take millions of years to occur and jump straight into space ships! These little guys will fly around shooting up enemy space ships and asteroids alike, simultaneously helping you out and being a huge pain in the ass (you want to absorb the asteroids they blow up!).
I could go into great detail about the rest of the games' "evolutionary" levels, but basically it goes like this: Life Planet > Small Star > Medium Star > Large Star > Neutron Star > Black Hole. The game increases in complexity once you hit the "large star" phase as you'll be dealing with up to 10 orbiting planets in your haphazard solar system, each with their own development process, gravity fields, ships, and so on. Once you reach the Black Hole phase the complexity of the game vanishes entirely and all you can do is fly around and destroy the universe. I'm not even kidding.
Suffice it to say that there are some really difficult missions to complete in the game, and there are rewards for beating the game (like physics tools and god options and whatnot), and the game is currently all of five measly dollars on Steam, so you should buy it without a second thought.
Seriously. Go buy it. Right now.
To further drive home just how awesome he is, the developer Murudai has released the game's excellent OST for free. So you should go get that, too.