Why can't I see my iTunes playlist in iPod?

I connected my iPod touch device to the PC to sync (manually) my iTunes music (mainly from the playlist). I dragged and dropped my pre-defined playlist into my iPod device on iTunes in my PC. While this playlist shows under my iPod device, I cannot locate the playlist in iTunes on my iPod. Why is this?

Am I missing something? Am I doing something incorrectly? Please advise as I am somewhat new to iPods. Thanks.

Sincerely,

John J. Bottiger