If you see an RSS (Really Simple Syndication) icon like this  on a web page, it indicates a feed of updated items that you might want to monitor.

Unfortunately, your browser may handle these feeds in a way that I find is less-than-useful - I prefer to see feed items in my mail client rather than in my browser. This is easy enough to fix, you just have to add the feed directly to your RSS-enabled mail client.

Why I prefer the Mail interface

Mostly because I think of 'new things to look at' as belonging in mail. The same 'check for new items' processes that get my emails can also check my feeds, so I only have to look in one place for new entries.

Although I receive RSS feeds like email, the feed provider doesn't know this - they never see my email address so I don't have to worry about more @#$% spam.

Making it work

Right-click the RSS feed icon  and 'Copy Link Location' or 'Copy Shortcut', then in your mail client (or RSS reader), create a new feed and paste in the URL link you just copied.

In Outlook 2010 there is an 'RSS Feeds' tab in the accounts setting form (File/Info/Accounts/Account Settings).
then

In Thunderbird there is a 'Blogs and News Feeds' account type.

In either cases you use the same sort of processes for adding RSS 'accounts' as for other entries.

When doesn't this work

Not all email clients support RSS feeds [1]

In a corporate environment, there may be policies that either restrict or prohibit adding RSS feeds to your mail client configuration.

Alternatives

Use your web browser. IE, Firefox and Safari all have some built-in support for RSS feeds. Chrome doesn't seem to – this is apparently a feature [2].

Use a specific RSS reader package on your PC (or tablet, iPad, phone, microwave etc). Because RSS is a standard, there lots of software packages that support it. Some stand-alone RSS readers support the same sort of 'new item' alerts and automatic checking processes as are found in email clients.

Use a web-based service (gmail or similar) as an RSS reader.

References

[1] Wikipedia article about RSS support in Email clients 

[2] Wikipedia article RSS support in browsers