I think the previous two responses covered it pretty well. Essentially the levels are a guide as to how much you've learned. For social dancing, you just go out and do stuff. However, it can help to know what steps are at what level because as joelwood said, you tend to dance at the lower level of the two people in the couple. For competitions, they determine what steps you can dance and it makes sure that everyone else will be doing the same steps. It helps keep a level playing field so that you're not dancing against people far better or far worse than you. They're also used for teaching exams. Organizations like the ISTD have exams for teachers at the various levels and the teachers need to know the technique and be able to dance all of the steps at the level they're testing for.
In a general sense, Keh is also right that bronze is like beginner, silver is like intermediate, and gold is like advanced. As you go up in levels the steps do tend to become more difficult or complex in some way. But this isn't exactly a hard and fast rule. For those who know the steps, an example would be having the Double Reverse Spin at bronze level in waltz, but Open/Closed Telemarks at silver. The Double Reverse has a syncopated timing, trickier footwork, and greater degree of turn. The Telemarks have straight 123 timing which means simpler footwork and less turn. So why is the Double Reverse bronze? One theory I've read is that they give you some of the harder stuff first to make the other stuff easier later. Following on that example, if a beginner is used to doing Double Reverse Spins, then it's easier to lead her into a Telemark. If she's used to Telemarks though, leading a Double Reverse can be more difficult. Hence, they give you the Double Reverse first. Anyway, I've also read that the levels introduce various topic/technique points. Bronze teaches all the basic stuff, when you start doing silver you get more OP partner position and such, and at gold you get things like picture lines.
So have we helped out or are you more confused than before? 
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James Marshall
marshall@astro.umd.edu
http://www.astro.umd.edu/~marshall