The word Liturgy comes from the Greek word Leitourgeo. Usually it’s defined as the people’s work. Which can be misleading if not explained. Leitourgeo actually refers to a public service done for the benefit of others. It includes the people's work, but the focus isn't on the people but the public service done for others.
For example, the State builds roads and bridges for people to travel on. The taxes gathered are used to do this. But it's done for others. Liturgy is a public service done for the benefit of someone else.
In the Divine Service God is doing liturgy to us as we respond in liturgy to Him. Lutherans are gathered for Divine Service to receive God’s public service on their behalf, and to respond in public service to Him.