I asked a gathering of home-group leaders this question: Can you give me a single word that sums up what you think your small group is about?
The answers were varied and interesting. We had caring; fellowship; worship; growth; love; and several others along the same lines. The slightly surprising answer I shared to that question was the one found in Hebrews 10.23-25: ‘Let us hold unswervingly to the hope we profess, for he who promised is faithful. And let us consider how we may spur one another on toward love and good deeds, not giving up meeting together, as some are in the habit of doing, but encouraging one another—and all the more as you see the Day approaching.’
Encouragement
As far as I can tell, this verse in the NT is the only one which actually commands us to meet together as believers. It doesn’t specify what day, or in what numbers, or in what set or subset of the local congregation we should meet. Simply that we should not neglect doing so, and that the purpose of our meeting together is for mutual encouragement. But encouragement for what? The context of the verse tells us.