Gemini is an alternate, in development, hypertext protocol for Internet-based documents. A bit nicer, and more secure, than Gopher, but much less featured than HTML.
The whole thing is really nice and clean, and easy to understand. A 'gemini file' is a text file that permits a small amount of markup, for links, lists, and pre-formatted text. Gemini documents can link to Markdown files, HTML, images, and other media.
I've been using Bombadillo, which also works with Gopher.
A key part of Gemini, and an important difference with Gopher is the mandatory use of security certificates. Think how on the web HTTPS is now almost ubiquitous. Gemini uses the same kinds of certificates.