A Redress number is a unique number that you can request from the US Department of Homeland Security. It is used for problems such as delays and denied boarding by the airline, entering/leaving the US or the repetition of a security check if your name coincides with that of a person on the US watch list.
If you think your name has been mistakenly linked with that of a person on the US watch list and you want to avoid identification problems in the future, you can request a Redress number.