The reasons behind the replacement program are over overheating batteries and safety risk for batteries with a manufacturing defect used with this series.
However, this program does not apply to any other iPod it only for iPod Nano (1st gen). And to check whether your iPod Nano is from 1st gen, the 1st gen was released with white or black plastic front and a silver metal back.
And Apple will then check your iPod nano serial number in order to verify whether your device is qualified for the replacement program. If it is, the replacement will be sent to you aprox 6 weeks after Apple receive your iPod Nano (1st gen).
Previously this replacement program only available for affected units in Japan and South Korea in 2009. But now, it's available for worldwide. You can visit this Apple Support Forum link to submit a claim form and find out whether you are eligible for this replacement program.