A bow's BRACE HEIGHT is simply the distance from the string to the pivot point of the bow's grip. You can think of brace height as how close the string will be to your hand (on the hand holding the bow) when the bow is at rest. The closer the string is to your hand, the more work you have to do to get the bow drawn back, since you're starting off farther away from full draw. Of course, pulling a longer powerstroke usually means more speed and power. As a general rule, shorter brace heights yield faster speeds. Taller brace heights tend to yield slower speeds.
But like many things, there's a trade-off to consider here. Short brace height bows are generally less forgiving and require more skill to shoot accurately. Taller brace heights have the opposite effect, limiting the effects of form glitches. So if you're a skilled shooter, you'll probably have little trouble managing an aggressive 6" brace height bow. If you're just learning or have mediocre skills, a little taller brace height will yield better accuracy in most shooting situations.
The average new compound bow has a brace height of approximately 7". In fact, 7 inches seems to be the magic number for some reason - not 6-3/4" or 7-1/4" - but exactly 7". Consumers often see this as the "optimal" brace height - the perfect distance which yields the best blend of forgiveness and performance. Read more about this concept in our Compound Bow Selection Guide.
Whether 7 is in fact the "magic number" or not, over half the bows on the market have 7" brace heights. Bows with 6" brace heights are generally considered to be performance/speed-bows (except when it's a women's or youth bow), and bows with 8" brace heights are generally considered to be competition bows. Anything outside of that 6-8" brace height range is really considered a special-purpose bow.