Final answer:
The phrase indicates that the church is a living entity (organism) composed of individuals and also a structured system with specific roles and hierarchies (organization), reflecting its dual role as a community and an institution.
Step-by-step explanation:
When we say that the church is both an organism and an organization, it implies a dual nature. As an organism, the church is seen as a living, breathing entity that grows and evolves; much like a biological organism made up of many cells that combine to form tissues, organs, and organ systems, the church is composed of individuals who come together to form a unified body with a common spiritual life and purpose. On the other hand, as an organization, the church has a structured system with defined roles, responsibilities, and hierarchies, similar to the way living organisms are organized into efficiently functioning systems. This organizational structure within the church has at times mirrored historical institutions, such as the ancient Roman military, and its role in society can be understood via sociological terms like ecclesia, denomination, and sect.