Here is the info straight from the watchtower cd-rom:
Watchtower 85 4/15 pg 30-31
Situations that call for ‘marking’ are more serious than the above example involving children. Occasionally a person in a congregation pursues an unscriptural course that is very disturbing, though it does not yet justify the disfellowshipping action mentioned at 1 Corinthians 5:11-13. Such conduct occurred in the congregation of ancient Thessalonica, so Paul wrote: "We hear certain ones are walking disorderly among you, not working at all but meddling with what does not concern them."—2 Thessalonians 3:11.
What were other Christians in Thessalonica to do? Paul wrote: "We are giving you orders, brothers, in the name of the Lord Jesus Christ, to withdraw from every brother walking disorderly and not according to the tradition you received from us. For your part, brothers, do not give up in doing right. But if anyone is not obedient to our word through this letter, keep this one marked, stop associating with him, that he may become ashamed. And yet do not be considering him as an enemy, but continue admonishing him as a brother."—2 Thessalonians 3:6, 13-15.
Thus, without naming the lazy meddlers, Paul exposed to the congregation their serious course. All Christians who were aware of the identity of the disorderly ones would then treat them as "marked." The counsel, "keep this one marked," used a Greek word meaning "be you putting sign on," that is, ‘taking special notice of someone.’ (New World Translation Reference Bible, footnote) Paul said, "Stop associating with" the marked one "that he may become ashamed." Brothers would not completely shun him, for Paul advised them to "continue admonishing him as a brother." Yet by their limiting social fellowship with him, they might lead him to become ashamed and perhaps awaken him to the need to conform to Bible principles. Meanwhile the brothers and sisters would be protected from his unwholesome influence.—2 Timothy 2:20, 21.
The Christian congregation today also applies this counsel. The Watchtower of February 1, 1982, page 31, stressed that marking is not to be done over mere private opinions or when a Christian personally chooses to avoid close association with someone. As shown by the case in Thessalonica, marking involves serious violations of Bible principles. First the elders try repeatedly to help the violator by admonishing him. If the problem persists, they may, without naming the person, give a warning talk to the congregation concerning the disorderly conduct involved, even as Paul warned the Thessalonians. After that, individual Christians would keep the erring person "marked."
Good judgment is needed rather than predetermined rules about every aspect of marking. Paul did not give detailed rules regarding that problem in Thessalonica, such as stipulating how long someone had to have been refusing to work before he could be marked. Similarly, the elders are in touch with the flock and can use reasonableness and discernment in determining whether a particular situation is sufficiently serious and disturbing so as to require a warning talk to the congregation.
One purpose of marking is to move a disorderly Christian to feel ashamed and stop his unscriptural course. Individuals who had marked him, particularly the elders, will continue to encourage him and note his attitude as they have contact with him at meetings and in field service. When they see that the problem and attitude necessitating the marking have changed for the better, they can end their limitation as to socializing with him.
Consequently, marking should not be confused with a personal or family application of God’s advice to avoid bad association. While marking is not something that is needed often, it should be plain that marking is a Scriptural step that is taken when it is warranted, which step our Thessalonian brothers took.
[Footnotes]
See The Watchtower, May 15, 1973, pages 318-20.
For example, elders should exercise discernment in dealing with a Christian who is dating a person not "in the Lord."—See The Watchtower of March 15, 1982, page 31.