Holding space is something we can do for ourselves and/or for others. It is the act of providing two things: a boundary, and room within the boundary. This is key for learning and growth, to have both space to explore and a boundary to that space.
In holding space for ourselves and others, our ability to do so usually comes down to the quality of our breathing. Short, shallow breaths mean that we literally cannot hold space within our bodies. This translates to a lack of space we are able to hold emotionally for ourselves and others.
Deep breathing if forced is not necessarily good for holding space. If you are forcing your breath, you are forcing other things, and that will be transmitted to people around you, who will respond by rebounding that force back on you.
Deep, easeful breathing is good. This happens naturally when we are in a positive, relaxed emotional space, feeling strong and confident in who we are. It can also be brought about by the practice of smooth breathing.
Try this: take a few deep breaths, and look out for the moment when the breath begins to become effortful, meaning it stops being easy. To take a small breath is easy. To take a deep breath is hard. At some point, there is a transition between ease and effort. Find this point. Then breathe in again, this time just below the point where tension arises and you have to start putting effort in to force the breath to expand more. When you get close to, but not actually to, the point of effort, slow down the inhale, and relax. This will naturally lead you to exhale. This is a way to begin the practice of smooth breathing. Try not to hold the breath at all, in any way, at any point in the process. If you get just one smooth breath, rejoice.
Practicing smooth breathing will allow you to take deeper breaths with less effort. This will allow you to hold more literal space inside your thoracic cavity, which will translate to greater ease of being in yourself and greater ease of being around other people.