There are different formats of feeds like RSS, Atom etc. The purpose of feeds is to make content syndication easier. You have bunch of articles or blog posts to share, you simply create a XML/RSS and share it with others. There are readymade tools availabe that will help you create Feeds. There are tools for readers that will convert Feeds into articles.
So what can a Feed do for my website?
Feeds are useful in a number of different ways:
* Your subscribers will come to know about new blog post/articles as soon as its published.
* As feeds are delivered directly to your subscribers, they will 100% reach them without worrying about SPAM Filters.
* RSS feeds by nature are viral. Just imagine if your user is using Google Reader or something similar, their friends will also see same articles. This can give you viral traffic and boost your online business.
* Another Benefit is that you can use someone else's feed on your website that may help you engage your readers. This way you don't have to spend time writing on the articles instead you can use someone else's feed.
* Search Engine will love your website if you are using relevant feed as there is fresh content for them to index.