To be fair to Mason, the answer is mostly listed in the first line of the introduction.

    mason.nvim is a Neovim plugin that allows you to easily manage external editor tooling such as LSP servers, DAP servers, linters, and formatters through a single interface.

I still use Packer, so perhaps that is not true for Lazy, but the other package managers handle Neovim plugins, mostly GitHub repositories with vim or lua codebases.

Mason installs and manages things like Language Servers, which are separate binaries running on your machine, and also starts them on demand.

I consider Mason integral to Lazy, some plugins require additional tools that should not be bundled like linters and formatters, and Mason is the best way to manage these.

Lazy.nvim uses mason to install some components.