Apelaunō means to drive away, expel, or force someone to depart. It combines apo (from/away) with elaunō (to drive). In Acts 18, Gallio drove Paul's accusers from the judgment seat — an act of Roman judicial dismissal that actually protected Paul and advanced the gospel.
Gallio's dismissal in Acts 18 is a remarkable example of how God uses secular authorities to protect the gospel. Gallio cared nothing for Jewish theological disputes — his indifference became Paul's protection. The advance of the gospel is often served by unexpected instruments. God's sovereignty is not limited to the actions of the willing.