Breathing from your core is important in any exercising that you do. It's especially important in water aerobics, because it makes your workouts more efficient.
A lot of people don't know what core breathing is, so let me give you a little demonstration. Pretend that there's a pool of water in your belly. You want to suck the water out through your core, through that tube in your core. It explodes through your chest, and then the water drips back down.
So, if you think about that when you breathe, you're going to be able to breathe from your core, better. A demonstration would be breathe in, fill your belly up with air, it comes all the way up, breathe out, and it drops back down.
When you're doing this with weights or any of your exercises, it will make it more efficient. So, we breathe in, and breathe out when you push back down. So, we breathe in, and exhale through the mouth. You want to make sure that you breathe in through the nose, and out through the mouth. And that is core breathing.