"
Free Dining" is simply one of several promotions/discounts that WDW offers fairly regularly. Essentially, it offers a dining plan (which one depends on the level of your resort... Quick-Service for Values, regular for above) with a qualifying package. Note that, expect in ultra-rare cases, you cannot combine resort discounts. So, you cannot take a room discount (percentage-based) along-side the free dining plan discount.
Can you add it? Possibly. If your check-in date is within the window on the offer (check-out date doesn't matter for packages here) AND there's room at your resort and room level, you should be able to add it to your existing reservation. Also note, there historically has been a 3 night minimum stay requirement along with the ticket requirement (see below).
Packages? A resort package includes the resort room
and park tickets. The free dining promotion
only applies to resort packages, so tickets must be added to qualify. Typically, the minimum ticket length is 2 days, but this could always change. The dining plan itself, however, no matter the length of the tickets, always pertains to the length of your stay (by night). So, if you go for 6 nights, but only get 2 day tickets, you'll still have 6 nights worth of dining plan!
Package rules? There are specific "rules" and policies for packages, which may affect your decision. The biggest ones are the required ticket purchase, and the payment dates (ticket purchase already covered

). For all packages, you are required to submit a $200 deposit at the time of booking. This deposit is fully refundable until you reach 45 days before check-in. At that time, the balance for the rest of the package comes due (you can make payments on the package throughout).
To Qualify? Essentially, to qualify for this discount, you simply have to book a package that checks in within the window (you can stay past the end, but you cannot check in on that package before it starts and get free dining), you have to purchase at least the minimum ticket requirement for the discount, and you have to stay at least the number of nights (typically 3) stated by the offer.
It all sounds a bit complex, but if you see the offer open up for your dates and you want to take advantage, simply call Disney up and they'll verify all the qualifications (and try and upsell you on stuff...but that's beside the point) and see what they can do for you.