Awareness, mindfulness, here and now, all those practicing meditation come accross those words, now I am finding about "focusing", which, btw, looks to merge just fine with practice circles. That's how focusing describes presence:

It does not want to fix
It does not want to solve
It does not want to get rid of anything
It does not want to push for a resolution
It does not hate this or love that
It can be with anything for as long as it takes and does not push
It can be with anything!
It has no agenda for how things should be or unfold
And much more besides…

Looks familiar?

Some links:
http://www.focusing.org/
http://www.focusingresources.com/index.html
http://www.focusing.co.uk/