The sites that RSSBot submits feeds to are called "RSS aggregators". They collect (aggregate) RSS feeds and make these feeds available to others that may want to access them. These sites usually include some type of directory and/or search capability for people to find RSS feeds that they may be interested in using.
When you "ping" a site (it doesn't have to be JUST and RSS feed), you are sending a "notification" to a service that this site has been updated. Most of the RSS aggregators can also be "pinged" (to tell them that your RSS feed has been updated). Google (and all the other spiders) constantly crawl these ping sites checking for updated information. When they see a notification on a ping site that your site has been updated, they will (often) in turn crawl your site as well to update their indexes.
"Pinging" is useful to ensure that the search engines have the latest version of your site in their indexes (as well as helping you get a new site indexed).
"RSS Submission" is useful for backlinking purposes. Your feed contains links back to your site, so each aggregator that has your feed stored on their site is providing backlinks for you.