TL;DR: Gopher is an internet protocol that was popular for a brief period before the World Wide Web rose to popularity.
In a nutshell, Gopher is an early internet protocol. It's a lot similar to FTP in general usage, providing a list of files to download and directories to browse through using hyperlinks. It's completely text-based too, making it an easy choice for browsing some form of internet via a terminal or otherwise retro desktop systems. We clearly don't use this system nowadays, as it was only popular before something known as the World Wide Web became the next big thing. Such a big thing, in fact, that it's practically synonymous with the internet - plus, you're using it to view this page! (...but you probably already knew that.) The protocol sharply dropped in popularity thereafter, and so did browser support, pushing popularity down even further. At its lowest, there were only ~100 known Gopher servers running.
...But it's not quite dead yet!
Nearly 400 Gopher servers were indexed in January 2020, a roughly-4x increase since 2007. I once contributed to this increase by hosting a Gopher site alongside this site, however the text-based nature of Gopher made it difficult to port things over. There are, however, other Gopher sites maintained by people like me; you'll just have to dig to find them as I have yet to catalog some here. If you want to check them out, you'll need a browser that still has support for the protocol, or a plugin for your current browser. I've listed a few good modern choices below:
(Note: "*nix" is an umbrella term for Unix-like systems, such as Linux and macOS.)
|OmniWeb||macOS||Recently-discontinued macOS-only web browser by The Omni Group. Native support for Gopher.|
|Dooble||*nix, Windows||Privacy-oriented web browser. Native support for Gopher.|
|WebPositive||Haiku||The bundled internet browser of Haiku. Native support for Gopher.|
|Lynx||*nix, DOS, Windows||Commandline web browser. Native support for Gopher.|
|ELinks||*nix||Commandline web browser. Support for Gopher requires building with the option selected, even then it's experimental.|
|Mainstream Browser||Plugin Required|
|Firefox||Either one of the Overbite plugins: One for native support, or one that uses a proxy.|
|SeaMonkey||The legacy version of Overbite.|
|Chrome||Burrow. Uses a proxy.|
If you'd like to learn more about Gopher, check out the Wikipedia page about it.