Why the Name?
Drinking Hoppy in an izakaya (Japanese pub) is one of my favorite things to do when visiting Tokyo and is so quintessentially local that I think everyone should try it.
What is Hoppy?
Hoppy is a tasty beverage produced in Japan and particularly popular in Tokyo. It's considered a shitamachi (downtown) thing and you'll find it in bars and izakaya all over areas like Asakusa and Ameyoko.

There are two main kinds of Hoppy, shiro (light) and kuro (dark). It's generally mixed with shochu (a Japanese distilled spirit, sort of like vodka but not quite as high proof in general) in a 5-to-1 ratio to make sort of a highball. It tastes malty and vaguely beer-like. It was originally developed and released in the late 1940s as a substitute for beer which was generally way too expensive for the working class.
When it comes to drinking Hoppy there are pro- and anti- ice camps. I personally prefer it without ice but will make an exception when it's stupid hot outside (i.e. August...).
As far as ordering Hoppy or refills, the big words to remember are 'naka' and 'soto'. The shochu is referred to as 'naka', meaning 'inside', and the Hoppy is called 'soto', meaning outside. When you get your first glass they will bring a glass or mug out with the naka already inside and you add the soto to your preference. When adding the soto to the naka be sure to pour it in quickly so it foams up. After you drink what you have and want some more you can order more shochu, "Sumimasen!! Naka!!", or Hoppy, "Sumimasen!! Soto!!". Trust me, it takes a while to get used to shouting for service in an izakaya but a couple rounds of naka and soto will help. I personally usually do two naka per soto, so basically two rounds of shochu to one bottle of Hoppy.