"Airplane Mode" turns off all wireless communications on the iPhone completely. No 3G, no wi-fi, no bluetooth.
You can turn on and off Airplane Mode in the iPhone settings -- first option, at the top.
You'll be able to tell if Airplane Mode is on or off by either the presence or absence of a little, orange airplane-shaped icon at the very top of your phone's screen, next to the battery meter.
When you first turn on Airplane Mode, your wi-fi connection will be disabled. You can re-enable the wi-fi connection only (so you don't have to worry about airtime charges) by visiting the "Wi-Fi" settings and turning wi-fi back on... that way, you can connect to 802.11 wireless access points and hotspots, but not the 3G, EDGE, or CDMA network.