The article explains three ways to get new comments in a thread. One way is to go to Algolia (Search provider for HN) and type in the thread id in a specific format. This bookmarklet will open that page directly with all the options pre-selected instead of having to open a new tab, copy and type in the id in the search box, etc.

Algolia is the search that HN uses when you use the search bar at the bottom of the page.

algolia is the search provider for HN. If you use the search bar at the bottom of HN, it will take you to algolia.