What is a VPN?
A VPN or Virtual Private Network provides an encrypted tunnel between two computers on the Internet. Each computer uses a shared secret to encrypt all data between them. Unlike a proxy service, once a VPN is established, all incoming and outgoing traffic between the two hosts is encrypted. It therefore encrypts not only your web browsing, but also your email, skype, VoIP etc. Most importantly, your ISP or anyone for that matter, cannot log, view, or control your Internet activity whatsoever.
From the perspective of websites and other services on the Internet, when you are connected to the VPN your traffic will appear to originate from the VPN server. Therefore, if you connect to a UK VPN server your IP address will appear to be a UK IP address. Your actual IP address and location will be completely hidden and impossible to determine unless you voluntarily give this information out e.g. when completing an online form etc.
In the diagram above, there are two users, Alice and Bob. Alice is not using a VPN service whilst Bob is connected to iVPN.net. Both users are browsing 'news.com' and 'forum.com'.
In Alice's case, her traffic is flowing through the ISP without any encryption and so the logs record exactly where she is connected. The servers to which she is connected also log her real IP address affording her no privacy.
In Bob's case, he is connected to the iVPN.net server and therefor all traffic through the ISP is encrypted. The ISP can only record that bob is connected to the iVPN server, nothing else. The servers to which he is connected think that it is the iVPN.net server which has connected to them and so they can only record the IP address of the iVPN.net server in their logs.