VPN is one of those things that if you don't know what it is, then chances are you don't need it...
As others have mentioned above, it's a protocol used to allow access through corporate firewalls by creating a securely encrypted "tunnel" between your device and the corporate network. Once you've established a VPN connection to your corporate environment, you can generally access web portals and e-mail servers within the corporate environment as if you were sitting on your desktop computer at work -- your device essentially becomes connected directly to the corporate network (that's a bit of an oversimplification, since different companies configure their VPNs differently, but that's the general idea).
The iPhone only supports a PPTP/L2TP VPN, which is a common lower-end VPN solution used by many inexpensive routers and Windows Servers. More sophisticated VPN solutions generally use IPSEC or some variant thereof, which the iPhone does not presently support. Chances are that if you have to add a special client to your laptop to get VPN access to your corporate network, you are either using IPSEC or some other proprietary VPN technology, since Mac OS X and Windows 2000/XP/Vista have PPTP/L2TP VPN capabilities built in.