These fare are designed to allow Thai nationals living overseas  to return to Thailand cheaply. Actually Thai Air isn't the only Asian airline to offer such fares. Philippine Airlines also offers discounted airfares for it's citizens living overseas to return to their country. So if you qualify, this is a great way to get cheap airfares to Asia. The beauty of these fares is that family members can also travel to and from Thailand on deeply discounted airfares.

Thai Airways in each country will have it's own promotional fares which they sometimes call the "sawasdee fare". Of course conditions do apply, the main one being that in order to take advantage of the cheap airfare to Thailand, non-Thai family members must travel with the Thai family member. You may also be required to provide proof of your relationship, however in most cases, having the same surname should be sufficient.

Another thing to keep in mind with this type of discounted airfare is that being so cheap, they most probably will not earn any miles if you are a member of a frequent flyer program, or if they do earn miles, you will only earn a small percentage of actual miles flown.
Utilizing these types of discounted airfares is a little-known great opportunity to get cheaps airfares to Asia.

Update: September 24th 2006

Recently a number of people have contacted me saying that they were unable to obtain these special fares in their country of residence.
Unfortunately the threat of lawsuits has killed this offer in some "politically correct" countries. When people who were not eligible for such offers found out about them, they threatened legal action against Thai Airways on the grounds of discriminative pricing practices.