"It is a group of people who are committed to Jesus and committed to one another, sharing their lives together and sharing mission together. It is about people hanging out together, doing chores together, eating together, serving in the neighbourhood – all with gospel intentionality. That intentionality includes both a commitment to discipling one another with the gospel and sharing the gospel with unbelievers – all in the context of ordinary life and shared life. It’s not a meeting your attend. It’s not a thing you do. It’s who you are are. It’s your identity. It’s your place of belonging."
And then meeting in some shape or form centred around: meal, ministry and mission.
I highly recommend Steve Timmis on the same subject at resurgence, video talks with Q&A. Total Church Lectures by Steve Timmis An exercise he suggests is to re-read the New Testament and read references to church as the word "gospel-community" - it gives a freshness to thinking things through.
Chester and Timmis' book Total Church is the one that I turn to when I think about leading a church homegroup or training students in CU groups. It brilliantly models a three-fold agenda of being gospel-centred by being word-centred, mission-centred and community-centred.
In the autumn I'm hoping to help my team raise the bar on our CU training which can all too easily just be 'how to do a good Bible study' which is necessary but not sufficient.