When we take a deep breath, we are creating space in our mind for a fresh start. That fresh start can contain a new idea, a new emotional state, or nothing. This nothing is the goal of deep breathing in meditation. Initially, in meditation, we breathe deep to keep the mind from holding onto ideas, keeping the mind neutral and open for insight. The longer we meditate, the slower our breathing becomes, albeit balanced. This is mind moving to the more subtle energy levels. Say you're at the gym, working hard. The breath is deep and fast, because we are fueling the physical body, which requires lots of energy. In meditation, as we move away from the physical, our breathing slows, as we don't need as much energy to sustain ourselves. Indeed, it is the body which still requires energy, while what fuels the mind isn’t in this dimension.
Breathe in deep. Take with it everything around you, be it negative or positive.
Breathe out, and transform the negative into positive and release it into the world.