Just to add to USirritated here, because I'm as bad at acronyms as the best of them here...

EEO's are as USi states, Elite Exclusive Offers which include some pretty uninspiring fare, such as 10% off rates, free ski hire or 1k or 2k extra points per stay. Some seem less than exclusive, such as stay 2 nights, get 3rd night free, which whilst a good offer is frequently available to all anyway, like as now with the global long weekend, so is hardly "exclusive". Other EEO's are more interesting such free meals, 30% or 35% off stays 7 days/week, free BonusBuck vouchers, etc etc. Most EEO's are specific to an individual hotel so this list is not nearly as attractive as it may sound, but if you're out that way...

The main thing we all mean here when talking about EEO's though is the BOGOF - Buy One Get One Free - on hotel nights. Simply book a standard publicly available rate for a weekend and using the EEO voucher tucked away in the Marriott Platinum/Gold offers part of the website you'll get the second night free. It is genuine and easy to do, but has to be done by phone via the Gold/Plat line. Most members agree its one of the major benefits of the scheme, and sets Marriott Rewards apart from the competition.

Indeed, you'll almost always find when EEO's are mentioned that they soley relate to the BOGOF EEO, since its way the most valuable and the certificate is published 3 or 4 times each year. Here on FT, EEO means the elite BOGOF scheme...