RSS stands for Really Simple Syndication, which is essentially a way to build your own newsfeed, with only the content you choose. It works thanks to a web feed that chronicles new content from a specific website. You then have a service or app (the reader part) which checks them for you, listing all the articles for you to read. The key advantage to this approach is that you are automatically offered new content when it’s posted, without you having to waste time constantly checking the webpage for updates.
One of the most popular RSS readers today is Feedly, which is super user-friendly while still offering a range of powerful features. If that doesn’t float your boat then some other options are Inoreader or NewsBlur, among many others.
If you are curious just how exactly to add an RSS feed into Feedly — like, say, this one for my blog (right-click and copy) — here’s a walkthrough to do so (you’ll likely need to use the second option).