“Simple church” and “house church” are similar terms. I have been looking into the “simple church” movement and I think it has some interesting points. I like the idea of home Bible-study groups and am involved in one myself. The setting of a home Bible-study group is a good way to introduce non-believers to a community of believers outside of a structured church meeting.
Here is the opening paragraph of what Wikipedia has to say about Simple church.
Simple church is a re-definition of church as a Christ-centered community established primarily on relationship both to God and to the other members of the group. The term “simple” is used to denote the movement of many traditional church characteristics to the category of non-essential, or even unhelpful, in this model of church. A simple church may meet anywhere, with or without religiously trained persons or “clergy”, may not have any formal liturgy, and little if any programmatic or institutional structures.
– Wikipedia: Simple church