Everything in boxing goes hand in hand. With out balance u just seem like a person @ dance floor who dont know wth he is doing.Very Important to the game.
I'm being lazy, so here's a link that pretty much covers most issues related to the role of balance in boxing: http://www.expertboxing.com/boxing-training/body-movement/76-how-to-improve-your-boxing-balance
Yeah a lot of my combos are weak because I was off balance. I think with me it has more to do with my footwork though, which at times is just simply shambolic.
I see a lot of MMA guys with horrible balance. They'll try to go for the knock-out punch with every SINGLE strike and almost always at the expense of keeping their balance. This is something I'll have to test on my next sparring session. I'm going to wait for them to throw a haymaker, I'll slip it and then push them off slightly just to see if they just faceplant onto the floor.
Poor balance leads to injury and very poor technique. It's very important. Watch a good fluid boxer and you'll see balance in both hands and feet.