Presence (noun) the state or fact of being present, as with others or in a place.
Mindfulness is an everyday capacity, not some kind of grand and esoteric state. Children, the elderly, and even those suffering from minor mental health issues can all develop mindfulness.
We can feel it immediately when someone else is mindfully present with us. Their phone is away, they look us in the eyes, and they listen.
After strengthening the muscle of mindfulness, you'll start to find yourself becoming more settled into being fully there with your children, partners, and others. More peacefully relaxed in a moment-to-moment awareness of them and you and what's happening around you. Less worried about more things you think you need, replaying this from that from a mind movie of the past or planning for a 'better' future. Anxiety lessens, blood pressure lowers, sleep improves.
It's not an unachievable fantasy world. It's simply mindfulness. And the best thing is, it's free.
Try this easy exercise to get you closer to mindfulness. Relax, take a deep breath. Move your attention away from thoughts, if thoughts continue to come, say hello, and watch them go. Do not judge them or get involved with them. The mere fact that you can identify that it is a thought, or the voice brings more present awareness to your sitting. Thoughts or the voice can be like strangers sitting next to you at a table talking. You simply block out the incessant noise.
Once you have a moment of space, you will begin to recognize this thoughtless space as presence.
Continue to find time in your day to practice this, and you will notice the space (presence) getting larger and larger.