This is a question I get asked regularly. Obviously, this won't be the exact answer for every church, but at our church small groups are fundamentaL to how we do ministry - so here's the 6 purposes I tell people:
#1 Pastoring and shepherding our people! We don't view what happens in the small group as just "gravy" to go with the real ministry that happens at the church building or by the "pastors". Rather - we use small groups to break people into bite-sized segments under a spiritual shepherd who will watch out and care for their soul. (See Exodus 18:13-23) In other words, we shepherd our people THROUGH small groups. Small group leaders are not merely Bible study leaders - they are how we pastor our people.
#2 Connection - We shrink the size of the church by getting people into gospel-shaped communities. I tell people all the time that until they get into a small group they are really just "free-agents" floating around out there at our church.
#3 Care - The first and main line of care is through our small groups! When I hear someone complain that no one "from the church" did ____ for them - I always ask about what their small group did. Usually it was A LOT! That's how "the church" does care here!
#4 Spiritual growth & development. People grow best in community. Growth is MORE THAN just learning! All of those other aspects that you need to grow require other people involved in the process. Not only this, but having a spiritual shepherd who really knows you and is looking out for the condition of your soul is crucial!
#5 Encouragement and support - Life is hard. We ALL get frustrated and discouraged. Most of us are ready to throw in the towel in some area (our job, or marriage, parenting, living out Christianity, etc.) at one time or another. We all need people who are speaking into our lives!
#6 Evangelism and mission together - This is an area we are growing in! At one time we saw small groups as a place for us to be refreshed and challenged and motivated. Then we'd scatter to try to impact our world. But we're getting better at teaming up together as a small group to do mission and ministry. Groups do service outings together. We do Backyard Kids Clubs in our homes for a week in the summer. Our ladies host women's summer studies in order to reach out to neighbors in our different neighborhoods for 4 weeks. We utilize a prayer board with non-Christians we are reaching out to. We invite these people to fun things that we do as a group and then work together to help love them into openness to Jesus. We even invite them to come play in our small group volleyball and kickball league! Nothing says "you need Jesus" like getting hit upside the head with a playground ball!!
Bottom-line: EVERYBODY needs to be in a small group - or you'll miss out on HOW WE DO CHURCH!