Under the new terms, Yahoo will now only depend on Microsoft for 51% of its search results and ads, leaving the door open for Yahoo to push users towards their own potential search offering for just under half of all searches conducted through its site. For Bing ads run on its site, Yahoo will now keep 93% of the revenue generated — up from the 88% share it was entitled to as part of the original agreement. Additionally, Yahoo can now use Bing's algorithm to display search results without displaying Microsoft's ad listings next to them. In this scenario, Yahoo would pay Microsoft a fee for the results, but wouldn't owe it any revenue for ads.
Finally, after October 1, 2015, both companies will have the right to terminate the agreement at any point for any reason. This is in contrast to the original terms, which stated that the agreement could only be terminated if certain performance goals weren't met.
In any event, it looks like the new terms favor Yahoo heavily. Particularly interesting is the company's reduced reliance on Bing to serve up search results. This could open the door for Yahoo to slowly build out its own search offering while retaining the ability to lean on Bing's algorithms for just over half of the searches conducted through its sites.