These are two related ways to organize the fast amount of information available to us on the internet.
RSS feeds bring content that we subscribe to directly to us without us having to to sites to see if there is new content. I can subscribe to blogs, hashtags on Twitter, key word searches in newspapers, other content where the owner has ensured that the site will have a "feed" that pushes content to readers.
This is a somewhat dated but still good explanation.
I use Feedly for my personal /professional RSS feed reader.
I use Inoreader (with a paid upgrade) to create the aggregated feed for our blogs on our course website.
Rather than book mark interesting sites to my computer or browser, I use a "social bookmarking site. The two best known are Diigo and Del.icio.us. With each, I have a tool installed in my browswers and on my mobile devices. if I want to save something, I click on that tool, save the site, and -- importantly -- tag it.
Here's an example: On twitter, someone posted a link to a new video site. I opened it, wanted to save it, so opened the diigo toolbar tool and tagged it. It looked like this:
My bookmarks are all then "in the cloud", where I can access them on any device.
I can also search by my tags.
I can also create a RSS feed for any tag. Our Class Resources page is filled with RSS feeds for tags in my Diigo.
And : You notice that I also tagged this site 566 (as well as "video"). When I want something to appear in the optional reading part of our syllabus home page, I tag it 566, and it goes to the rss feed I have set up on the syllabus.
Both these tools work well to help manage the firehose of information on the web.