The Greek word bema (translated "judgement seat" in the KJV) was a familiar term to the people of Paul's day. Dr. Lehman Strauss writes:

" In the large olympic arenas, there was an elevated seat on which the judge of the contest sat. After the contests were over, the successful competitors would assemble before the bema to receive their rewards or crowns. The bema was not a judicial bench where someone was condemned; it was a reward seat. Likewise, the Judgement Seat of Christ is not a judicial bench....the Christian life is a race, and the divine umpire is watching every contestant. After the church has run her course, He will gather every member before the bema for the purpose of examining each one and giving the proper reward to each" (Lehnman Strauss, God's Plan for the Future, Grand Rapids: Zondervan, p. 111)