AFAIK, there is (unfortunately) no official concensus on this matter. That aside, logic and speculation do help fill in some of the blanks.
- They're meant for training/fighting. - According to WiseGeek, bicep bands can be worn around the arm of someone doing physical activities to catch and absorb sweat. There has been rumors of how they keep constant pressure on tendons and thus would help keep in intact with the bone, thus preventing serious conditions such as tendonitis. Recent research, as the resource above states, has generally concluded against this, but during the time of Dragonball's production late 80's/early 90's, this would not have been known. Generally bands are not worn on the thigh, as he does, but again, since research had not been conducted, the writer may have just assumed it would have similar effects.
In addition to the this assumption, we could slightly speculate and say that they are similar technology, but enhanced in a way greater than our own world's limitations, but serve essentially the same purpose.
- They are a symbol used by Saiyan Warriors - The fan base enjoys looking for symbolism, and this is no exception. Many assume it indicates rank, or family. This assumption doesn't have much foundation though, since few, if any, other Saiyan warriors are shown to use them.
Most likely they're just decoration, designed to enhance his appearance. I doubt Toriyama thought this out very deeply. :)