I teach my confimation students to answer to this basic question: "What is worship?" The answer I'm looking for is something like, "God gives us gifts--we give Him thanks and praise." Worship is a rythmn, a back and forth relationship, with God Himself taking the position of primacy. His gifts are what make the Divine Service, they are the most important, they are what come first. But within the Divine Service, we have the opportunity to adore Him, to thank Him for those great gifts, to praise Him for His salvation.
Where does the offering fit in that spectrum? Well, it obviously seems to fall on the end of 'we give Him thanks and praise.' God has blessed us with the First Article gifts of this earth, and we respond by presenting to Him our firstfruits for the work of the Church in our community and around the world.
Why do we give offering? The answer we most often give is, 'So the church can pay for things.' True enough. The congregation does need to pay for a lot of things: pastor's salary, the light bill, insurance, etc. The congregation also has responsibilities to support the work of the church throughout the world, by supporting distict, synod, and missionaries.
But is that really the answer to why we give offerings? Unfortunately, and I know this as a pastor of small, financially struggling congregations, we can get caught up in thinking only in those terms. People give so that we can keep the doors open. But that isn't truly why we give; if we stay focused on the bills, then we lose sight of our end of the back and forth of worship described above. God gives us gifts and we give Him thanks and praise. We give offerings because God has blessed us. Indeed, we give in proportion to how God has blessed us. And we give especially because He who was rich became poor for us; we give in grateful thanksgiving for salvation and forgiveness.
We don't give so that the congregation can pay its bills, we don't give to a budget, we give according to how God has blessed us, whether little or much. God doesn't need our money, but we need His forgiveness, and then in gratefulness for that gift, we have the privilege to support the work of His Church