Short answer:
- You need a local Git server which hosts a clone of your example repository from GitHub.
If your local Git server includes a web UI, you can probably see something similar like what you see on GitHub.
- If you want future changes in the GitHub repo in your local repo as well, you need to pull periodically from the GitHub repo to your local repo.
Long version:
1. Hosting Git repos on your local server
There are a lot of options (paid and free) for running a Git server on your own machine.
Some of them contain web UIs which look similar (but not exactly the same) like GitHub.
There's only one option to get 100% the same look: by spending money for a private installation of GitHub (but it's not cheap).
If you don't want to spend that much, there are free alternatives, for example GitLab. This is a hosted service like GitHub, but the code is open source and you can install a free version on your local server.
Here's an example of a "repository overview" page:
https://gitlab.com/gitlab-org/gitlab-shell
GitLab is only one example, there's a lot more - just google for "self hosted git" and you will find plenty.
2. Getting a clone of the repository from GitHub to your local server
To set this up, clone the repo from Github to your local machine once with the --mirror
option:
git clone --mirror https://github.com/user/repo some/local/path
To update your local repo with the newest changes from GitHub, you need to run git remote update
periodically.