It's a wheat beer thing, for the most part. The term "hefeweizen", "hefe" + "weizen", means "yeast" + "wheat" in German. The yeast adds important flavor to the beer. I find it extremely delicious and my next brew will probably be a hefe.
edit: And on the gassy thing, I've never noticed drinking the yeast to make a difference. Your stomach's pH is so low that you're probably going to totally destroy any living yeast cells before they make their way past your stomach.