In the Name of the Father and of the Son and of the Holy Spirit. Amen.
Today's text confuses a lot of people, even a lot of Lutherans. It seems to be contradictory to everything else that we believe, teach, and confess. All that business about salvation by grace through faith in Christ alone – that looks like it gets chucked out the window with this passage. After all, the King is basing His judgment on the works done by those on His right and left. This seems to lend itself to the idea that you will be judged on the works you have done, whether you have done enough to merit the favor of the King.
The Church of Rome reads this discourse in just such a fashion. To them, this passage is all about hospitality that you must show to your neighbor. Your faith is formed by your love, which is worked out in your service to your neighbor. This passage is straightforward Law: do this, and go to heaven; fail, and go to hell. Salvation cannot possibly be grace through faith alone; Jesus commend these faithful for their works of hospitality and service.