This is one of the often-misquoted verses of the Bible. Many believe that this actually reads something along the lines of, "If a person doesn't work, he should not eat." This is not what this Scripture says. In this passage, the focus is not so much on what is done as on what a person is willing to do.
Paul wrote this near the end of his second epistle to the Thessalonians. He was reminding the Thessalonians of the example that he himself had set for them. In this same chapter of Thessalonians, Paul reminded the Thessalonians that he was already able to receive support from the church, since he was an apostle. However, Paul chose instead to set the example and work for what he received.
A question that must be asked of us all is this: Do we lead our Christian brethren by example? Do we go out of our way to set the example for them? Paul did. It is interesting that Paul did not have to labor for his provisions from the church, yet he chose to. The point was to set the example for everyone else.
We should all strive to set an example for out Christian brethren. Those who are weaker in the faith should be able to look and see a physical example of how to live the Christian life. Non-believers should be able to look to us and see what the Christian life looks like. The entire time, our actions should point everyone to Jesus. It is ultimately Him that they should see in us.