Your website will have to be able to subscribe to the blog's RSS feed, which will be available as one of the RSS feeds exposed by the Space's RSS feeds page:
1. From the main page (first one you get when you login) click on the Space's name.
2. On the right hand side, click on the link 'View RSS Feeds'.
3. The RSS feed you want will be called 'Blog Posts'. It should look something like:
http://<your_domain>/clearspace/community/feeds/blogs?communityID=<your community id>
Websites and other content management systems may have different mechanisms for 'aggregating' blog info via RSS feeds. Typically it involves providing the RSS feed URL.