Facebook describes the changes as being intended to "make it easier for businesses of all sizes to create and administer promotions on Facebook, and to align our policies to better meet the needs of marketers".
Most significantly, the requirement to administer promotions through a separate app (rather than on a brand's own page) has been removed, and companies are now free to run a promotion using either an app or through its normal Facebook page. The previous restriction was intended to protect Facebook from claims and lawsuits where its platform might have blocked a user's entry into a competition, but the company now seems to have responded to the chilling effect that restriction created, where some users were apparently nervous about using third party apps to enter a promotion.
The change means that creating and administering promotions on Facebook can be faster—and cheaper—and will allow promotions to be displayed in the newsfeeds of users who enter or like the page (meaning a better reach).
The new guidelines also relax the restrictions on the use of Facebook mechanisms (such as liking or commenting on content) as a means to enter or vote in promotions, and promoters may also now notify winners through a Facebook message (which was prohibited under the previous guidelines).
While far from universally observed, the old guidelines did create an extra administrative burden for promoters, as well as the lingering threat that a non-compliant promotion could be taken down by the platform.
It's still not a free-for-all though, and a number of restrictions remain: promotions can't require a user to post content on their own personal Timeline as a condition of entry, and can't tag or encourage users to tag themselves in photos in which they're not actually depicted. Promoters also still need to include terms and conditions which distance Facebook from the promotion, and include a complete release of Facebook from any liability.