How they use the Bloglines information is to "qualify" blogs for inclusion in their blog search. In other words, when you use ask.com's blog search, they only search blogs that are subscribed to using Bloglines. The idea is that this should raise the quality of the search results. Here's what they say about it:
Blogs and Feeds: Search the blogosphere using our unique algorithm that combines Ask.com search technology and Bloglines subscription data. We index the most popular blogs that people across the web subscribe to daily to ensure higher-quality results and minimizes blog spam.To try this, I searched for "apple wifi driver vulnerabilities" using Google, Technorati, and ask.com. Here are the results:
Even without going further than the first screen, I think ask.com has better results. But wait, there's more.
Look at the ask.com results. Do you see the little binoculars beside one of the entries? Hover over them and voila!
Without even leaving the search results page!