Yes. That's the suspended lever arm, which moves up and down as you move. You'll notice that the lever arm counts "steps" when you shake or move the pedometer. That, too, is normal — but it's not a very healthy way to get your steps in!
After a few days, you shouldn't notice the clicking noise. If you are among the small percentage of people who are annoyed by this noise, you may want to consider the the NL-2000 accelerometer or the NL-1000 accelerometer or the NL-800 accelerometer, which has a different mechanism for measuring steps. The NL-series accelerometers are completely silent.