It's a widget you install in the sidebar of your blog, that shows headlines from other blogs in your niche. Publishers who have the BlogRush widget installed are supposed to benefit from each other's traffic as visitors to these sites click on the headlines in the BlogRush widgets.
According to the BlogRush site,
“BlogRush was designed to be incredibly viral and to provide its users with tremendous distribution leverage to receive exposure for their blog content (onto related content blogs) that they could never achieve on their own; at least without a massive advertising budget.
“By adding the BlogRush Widget to a blog, a blogger can get instant distribution for their latest blog post titles across a network of related blogs.
“BlogRush users earn “syndication credits” (the right to have their blog post titles shown inside a widget on another related blog) based on their own traffic (loads of the widget) as well as the traffic of other users they refer to BlogRush. Users can automatically refer others to BlogRush via special links on the widget, as well as through the promotion of a special referral URL they are given.”
BlogRush may or may not be an effective traffic generator for you. You won't know unless you try it.
To find out if your blog qualifies you to apply for BlogRush, see BlogRush Terms of Service.
Blogs are manually approved (or denied) by the BlogRush staff, and are required to have at least 10 to 12 posts before applying.
If you meet the requirements outlined in the “BlogRush Terms of Service” link above, you should give it a try and see how it works for you.
If you find it isn't benefitting you after a trial period, you can always uninstall the widget.