Bema, is the greek word used for the judgment seat of a king, or governor, or some similar ruler with authority. The belief in two separate judgments is an attempt by some (rapture believing Baptists in my experience) to reconcile scriptural verses that clearly say we will be judged according to our works. This doesn’t fit with a faith alone theology where works don’t matter and salvation is a one time event which you can’t lose. 1 Corinthians 3:14-15, for example, talks about less than stellar Christians losing their reward and suffering loss, yet still being saved as by fire.
If any man’s work abide which he hath built thereupon, he shall receive a reward. If any man’s work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.
Most Catholics, I believe, see this as a reference to purgatory. A typical protestant reply is that this does not refer to purgatory, but rather to the loss of a reward (or crown) in heaven, and some believe this “loss” occurs at the bema seat judgment. The problem for the bema seat/reward argument is that Jesus was condemned to death from the bema seat (which Pilate sat upon) and Paul was accused before the bema seat of grievous acts for which the Jews wished him to be severely punished and/or killed. The bema seat is not merely a seat for handing out rewards, it is rather a seat for determining guilt or innocence and administering justice, including severe punishment and death. There is no bema seat judgment in heaven or on earth that only hands out rewards like an Olympic medal ceremony.