In a recent question posted to one of the blog forums I am a member of, a user wanted to know why a link to a feed should be placed on their site.
(Syndic8 forum can be found here although you may have to join to view the group).
The user in question had their blogs hosted with Blogger, who have an option to create the feed, make it public, but you must include a link in your template file if you want it to appear on your webpage.
On my own webpage you will see a link to a file called index.rdf .
This is my main feed for my site. One reason why you put these links on your site, is to allow people to syndicate your content. (Its where gets its name from).

First off, what is syndication?

Well simply put, syndication is providing content for other people to include on their own site.
For example I am viewing various blogs and I happen upon yours. I find your site very interesting and its content is similar to mine, relevant or just something that interests me.
I can take the short cut that you put on your site to your atom.xml file (in the case of Blogger), and I can using some third party code, display the content on my own site.
I can display just the titles, the titles and some of the content, or the complete feed.

If you have a look in the right hand column of my pages you will see content from various places, (Test Engineering Careers, ‘Tickling the Bone’, Syndic8, Blogrollin and BlogLinker).
In the left hand column I have content supplied from the BBC News website.

I have a script/utility installed on my site here so enter your feed link (your link to your atom.xml if on Blogger), and have a play with some of the options
and it will become a little more clear (hopefully)

Why else would you want to do this you ask???

Well, not only are you now displaying content from other sites, you are also displaying links to the content on their sites.
So if you look again on my website, and click on one of the BBC News Headlines, it will open up a new browser window at the BBC website.
Having lots of out bound links from your site helps to move you up the rankings on search engines.
Even more so if they are related to the content on your site, ( so in my case, the BBC links are not quite
related to my site, so it doesn’t impact my search engine rating here too much)
Likewise if you have provided a link to you atom.xml file on your own site and someone comes along and uses it to
display your content on their site,
it will now contains links back to your own site.
These are called inbound links and similar to above, these also improve your web site rankings.

This is a basic introduction into syndication, written as an attempt to explain the why fors, and what fors to a beginner. There is more to the subject that this,
and if I get time, I try and post a deeper article on the subject one day.