Is it safe connecting to an unsecured wireless network?

ok my question is that can the computer i'm wirelessly connected to see what i'm doing on the internet, even if my network & file sharing are turned off? i have a laptop with a wireless LAN connection, connected to a local area network, since i don't have my own wireless modem, i basically connect to theirs. i can only connect to unsecured networks & i also made sure that my network & sharing center are turned off so they can't access my files... but when i'm about to connect to a wireless unsecured network, it warns me by saying "information sent over this network might be visible to others". so what type of information would they might see? i have been using the unsecured networks for about 5-6 months now & i have never really noticed anything but i just want to make sure. it would even be easier just telling me what those people see when i'm connecting to their network. like would their computer tell them somebody is connecting to their computer?