in its meaning more attached to the material world, presence can be read as that capacity, not so usual or frequent, to be being.

it is being in a conversation and listening, it is following in the flow and speaking from what has been exposed, not from the idea that we have fixed in our mind and we need to let go, it is dancing with the flow of life, being aware of what the contribution of the other moves inside us and moving from there, presence is washing the dishes while we wash the dishes, going to mushrooms when we go to mushrooms, and to beers when we go to beers.
Presence implies stopping the mind, so travelling and so fiendish, and being here and now, without time or space, without past or future.
in its higher meaning it is that image of being above good and evil, a master and wise person, whose energy surpasses distances and fills all space.
This image of superior being can be represented by Yoda (in Star Wars), Master Oogway (in Kung Fu Panda) or Siddartha (Buddha).

the challenge in this characteristic is greater, not lesser, and lies in identifying which close person is an example for you of presence, that rare quality of being there.