The people were inspired to serve. They're inspiration came directly from the Lord. They got a glimpse of His true nature. In Exodus we read that the people had strayed from their relationship with the Lord. They made a golden calf and proceeded to worship it. After being confronted with God's displeasure concerning the matter, they repented of their deeds. God's goodness and mercy were revealed. He forgave them!
Now in Exodus 35:20 they are ready to serve. Not as a result of coercion but because of inspiration. God's goodness and mercy has inspired them to serve. They don't serve so as to be saved but desire to serve because they love the Father!