This is a good thing, but presents a challenge when the duration of a movement, like sparring in BJJ, last more than several seconds. When we hold our breath, we induce premature fatigue on our bodies. Our muscles need oxygen to work long and hard, the longest they can go without it is about 3 seconds. Holding your breath might get your core prepped for that submission escape, but it eon't help your working muscles continue long enough for many more subsequent move.
The technique of breathing is 'Inhale through the NOSE, Exhale through the MOUTH'. Breathing in throught your nose warms and humidifies the air entering your body. This makes consumption and oxygen extraction easier and more efficient for the cardio/pulmonary system. Less work for the lungs helps maintain a steady state that will prevent early fatigue. In addition, inhaling through the nose causes a reaction which produces nitric oxide (NO) in the nasal air passages. NO helps improve oxygen uptake in the muscles. That means you can spar longer and fight harder.
INHALE through the NOSE, EXHALE through the MOUTH