Anything with a higher density than water will sink in water.
The human body is, by weight, approximately two-thirds of water. That means our density is similar to that of water.
So why do we tend to float when we hold our breath, and sink when we breathe? For example when we go underwater while holding our breath, we try to touch the bottom, but it is very hard to do so because naturally, we'll float back up. However when we breathe out we tend to sink.
Well, oxygen is less dense than water. So, of course, the more oxygen you have in your body, the more buoyant you'll be. Hence, when you take a deep breath and hold it, there's more oxygen in your body and so you'll float since oxygen is less dense than water.