Home Groups are small groups formed from people who are seeking to relate with other Christians much the same way we read about in Acts 2.  These groups typiclaly meet in homes and their gatheirngs include relational fellowship, food / a meal, biblical study, and prayer.
 

They worshipped together at the Temple each day, met in homes for the Lord’s Supper,
and shared their meals with great joy and generosity.”

Acts 2:46