It's the one thing when I'm configuring things that makes me wince because I know it will give me the business, and I know it shouldn't, but it does, every time. I have no real idea what I'm doing, what it is, how it works, so of course I'm blindly following instructions like a monkey at a typewriter.
Please guide me into enlightenment.
Think of the Internet as being able to send opened letters with a destination address and return address. Anyone that handles the letter to help deliver it can see what it says, who's sending it, and where it's going.
A VPN is like asking a company to help you transmit the letter with more privacy. The VPN creates a secret code between you and the VPN, so that only you two understand what is in the letter. Then, the VPN communicates with whomever while not sharing your identity so that no one knows who you are unless you specifically tell them in the letter.
Say you want to know what the symptoms you're experiencing after a sexual encounter are, but you're embarrassed and don't want anyone to suspect anything in case it's nothing. You tell your VPN you want to send a letter to the medical info center. The VPN tells you to use a code that was created automatically so that no one knows what it means besides you and their code machine, and was sent to you earlier when you signed up for their service or at a regular update. "Use code 5 we sent you last week." You write the letter and address in code 5, then address it in normal language to the VPN, sending it via the mail system. The VPN machine translates the code to normal language but changes the return address to its own address. The medical info center receives a letter saying that the VPN wants to know the info you requested, so they respond. The VPN receives the info, translates it back to code 5, and sends the info to you.
As far as everyone in the mail system is concerned, you sent and received info from the VPN, but only you know what it was because the mail system couldn't understand it, and the VPN handled it through an automated machine. The medical mail system and medical info center then knows what the letter said, but thinks the VPN requested that info, so they don't know it was you. Since the VPN handles tons of mail, no one knows who is requesting what specific info through the VPN.
Note: This assumes the VPN doesn't keep logs. Some VPNs might actually track what you send, so they could keep track of your messages. That's why people that value privacy recommend to use VPNs that don't keep logs.