Ok, let's see, what's VPN essentially? According to the OSI model, IP packet is something like an onion with the multiple layers, wrapped one over another. The top layer contains the physical address of my network adapter. So my adapter sees this onion with his address stamped on the top, catches it, and passes it to the other parts of my network software. They begin to unwrap this onion, getting deeper and deeper inside. On the deepest layers lies the actual application data, for example, a message I receive from somebody.
So, the idea of VPN is that innermost application layer of the onion can be another onion. It goes like this: I have this VPN app on my computer, that talks to the VPN server somewhere far away, and we kinda exchange messages. The thing is, those messages contain a totally different exchange between another host and me on the Internet. The VPN server unwraps the onion I send to him, and inside it finds another onion. (The onion is encrypted, so nobody except VPN server and me can figure out what it actually is) The topmost layer of that second onion contains the address of the actual host I want to communicate to. Also, it contains my "alter-ego" address. The alternative IP I receive from the VPN server. This IP can be somewhere in Cambodia.
At this point, I see it, as if I have two internet connections: One is real - with the IP address assigned to me by my provider. Using this connection, I communicate with the VPN server. The second internet connection is Magic. Because it shows as some IP address located in Cambodia, although, I'm not in Cambodia, so I'm sorta perplexed how it can be. The thing is, the second Magic Internet connection exists within the first real connection like a fetus within a womb. In fact, if somebody traced my Internet traffic, he would see me communicating exclusively with the VPN server. Meanwhile, I normally browse the Internet and do all the usual stuff. So the trick is, that all my internet communication (inner onion) is carefully packaged, encrypted and sent to that VPN server (hidden in the outer onion), which, in turn, unpack it and does all the Internet exchange on my behalf. From that server in Cambodia. The responses are also neatly packed, encrypted, and sent to me, hidden in our private channel, between me and the VPN server.