:o The Wireless CompactFlash Network Card is just that... a network card. It will only let you access networks within ~100ft or so of a wireless Access Point or Router. Typical uses are for home networking, access at work, or at various public "hotspots" where they happen to offer such service, usually for a (ridiculous) fee.
It is not an "internet" card, per se. If the network you're connecting to also connects to the internet, then so will your Axim. But this card will not enable you to surf from anywhere. For that you need a wireless modem and wireless ISP service which, again can be had, but is very pricey. Another method is to connect your Axim to a cell phone, but this can also get expensive if you don't already have the equipment/service.
Here are some guides to help you understand wireless networking:
http://www.infopeople.org/howto/intro_wireless.html
http://www.envara.com/resources.html
http://www.howstuffworks.com/wireless-network.htm
Hope this helps,
--RHYNO