Before WordPress 3.5, there was a feature that allowed you to create and manage a set of links from your admin dashboard. To display them on your site, you needed to rely on a template that might or might not be included in your theme.
Bookmarks Shortcode provides a set of three shortcodes
[blogroll] that you can use in any post, page, or text widget to output a formatted list of your links. This is much more versatile than any template included in a theme as it allows you to place content around the list and remains consistent if you decide to switch or upgrade your theme.
You can read more about Bookmarks Shortcode and download it from WordPress.org. It still works on WordPress 3.5 or later, but you need this plugin to enable the links manager. And, as always, Bookmarks Shortcode has its own GitHub repository where you can browse the code, fork and contribute to it.