what is an airport base station and how does it work?

I received an iod touch for christmas and i am trying to figure it out. i have never used an ipod ever and know nothing about how it operates and all the things that it can do. i am having alot of trouble connecting to wi fi. i can connect at my job through a secure network. when i get home when i try to connect to an unsecure network that my laptop is connected to the ipod doesn't di