But the fellowship offering would be partially burnt on the altar with the remainder returned to the one making the offering and shared with the priests or friends. It was a celebratory offering meant to praise God and celebrate His provision and/or to ask God for His provision.
These were freewill offerings not given by command or obligation, but out of gratitude and faith in God to provide all that was needed. God instituted the peace offering as a way to promote fellowship with His people and among His people. The notion was that the people would give thanks for both what God had provided (the sacrifice) and believe in faith for what He would provide, by sharing what they had with priests and with others.
Let's think about that for a moment in our modern context. I got a new job. We went out to dinner to celebrate. Of course, we gave thanks to God for opening this opportunity and for giving me favor with those who made the decision. Maybe we invited friends or family to join in the celebration and paid for their dinner, trusting that through this new job, God had provided the means for us to do so. But do we stop and think about it in terms of our gratitude and our faith?
How often when we enjoy a time of special blessing from the Lord do we celebrate by sharing a portion of God's blessings with others? How often, when we are seeking for God to provide for a specific need, do we give generously to others in faith and anticipation that God will provide, rather than hoarding our resources to try to "help" God meet the need?