If you need to ask what a VPN is, you probably don't need one - not anymore.
A VPN (Virtual Private Network) is a way to secure all of your internet traffic (websites, emails, etc.) so it is encrypted and cannot be viewed by anyone. You do this by making a connection to some other network besides say the hotel WiFi's network. Companies run VPN services and let you subscribe (usually for a fee). E.g. if you are in Italy, you might subscribe to a VPN service back in the US and when you connect to it, no one in Italy can see what you are doing - all of your web traffic is encrypted and directed back to the US VPN company's networks.
I run a VPN server at home (most people don't, but it's pretty simple; runs on my router). So I don't have to subscribe to one. When I'm in Italy, I can connect to my VPN at home, and then all of my traffic gets directed through my home internet network. If you were monitoring my web browsing, you'd think I was at home, not in Italy.
In 2005 you might have wanted VPN, because most websites used SSL encryption. Back then, if you were on WiFi, people with the right equipment could view all of your web traffic e.g. web email, private messages, etc. (But not your passwords or credit card numbers.) Today, most websites are encrypted with SSL ("HTTPS"), so anyone with the right equipment trying to decipher your web traffic will see gibberish. At worst, they'll see WHICH websites you are visiting. So for example if you visit you credit union's website without a VPN, someone could tell that you are visited that website and guess you might have an account there. But they wouldn't get anything from what you are actually viewing on the site (not your username or account number or anything). They might find out this information in other ways anyway - e.g. you use your credit union credit card when checking in to the hotel.
I wouldn't recommend a VPN now to anyone but the most privacy-conscious user who is paranoid about people finding out anything at all about your internet activity. Even on an open public WiFi, your websites that use SSL are all being encrypted anyway these days , even without a VPN.