You've got two different directions going on here at the same time (grin):
RSS feeds FROM your website and TO your website. You can do both, but keep them separate in your head, or it will explode!
RSS from your website is a way to keep folks updated on new content that you post to your site. When you update your website with new content, your RSS feed also gets updated with the new item(s). How this happens (technically) is beside the point (could be database driven or maybe a 3rd party service).
People who are interested in your content, and see you have an RSS feed (you usually provide an icon with a link to the RSS feed/page/xml), and will subscribe to it using an RSS reader/software (3rd party, Google Reader, integration with browser or email client - there are lots of choices for RSS readers).
That's about it - once it's all setup and running, you update your website, RSS process updates the feed, RSS readers become aware of the new feed/content, and pull it into the reader, and subscriber sees new content.
It's not exactly the same as seeing it on YOUR website (they see text content, maybe an embedded image), but the young'uns like it because they can see updates to a lot of websites (with RSS feeds) from their central RSS reader.
RSS TO your website means pulling in other websites's content feeds (RSS streams) and presenting it on your website as content. A Mashup would be taking different RSS and other content feeds and 'mashing' them together in some meaningful way.
Ex: real estate site could take housing prices from one RSS, median incomes from another, and crime rates from a third, mash them up, and give an interesting picture of a neighborhood. Now, push all that into a mapping service (google maps) and you get a nice visual of the area!
Hope that helps.