The nano has a built-in pedometer, without the Nike+ sensor and receiver attachment . I don't think it measures distance, just the number of steps, which is used to calculate calories burned.
It says iPod nano (5th generation) in your your profile. If you already have a 5th gen nano (which I also have), it works great with the Nike+ kit (this one)
http://store.apple.com/us/product/MA365LL/F/Nike-iPod-Sport-Kit
It also works with the current 6th gen nano. With a sensor (accelerometer) that goes on your foot, it can do more. The receiver goes on the iPod's dock connector. It tracks more precise movement of your foot to determine pace and distance, not just the number of steps taken. I use it for running, but it should work equally well for walking. The iPod provides audible feedback of time, distance, and pace during the workout, and a summary (including calculated calories burned) at the end.
(It's not a GPS-based system that knows exactly where you are; it does not measure vertical change.)
When you sync the iPod with your Mac, the workout data is sent automatically to the Nike+ web service (once you "opt in" and set up your account), where you can log in and look at your data.
You don't have to wear special Nike shoes with a hole in the sole for the sensor. I use a "pouch" like this
http://www.amazon.com/Marware-Sportsuit-Sensor-Sport-Black/dp/B000ID6DTG
to attach the sensor to my New Balance shoes. It works fine. Actually, it works better because I can more easily more the sensor between pairs of shoes.