It's a badge with a little tab for each of the FP attractions in a park. You turn in a tab for one trip through the FP line for that particular attraction (and you also have to show the badge, too, with the tab). So, in DAK, which is where we won Dream FPs a few weeks ago, we had 6 tabs that cooresponded to the 6 FP attractions in the park. But, the kicker is you only get to use each tab once, so it's not unlimited rides on each FP attraction, just one ride per attraction. But on a crowded day, it can really be a great thing to ride rides you didn't think you could ride, and without having to get FPs out of the machines! We were especially happy, as it allowed us an extra trip on EE, since all the FPs were gone for the day and we didn't think we'd get to ride it again!
Each park's Dream Fast Pass is good for only one day and for only that park and only for specific rides. We won on Halloween in MK and it was so dead we didn't need to use even one. Many of the CM's told us to save them and use when the park was busy that they didn't really pay to much attention to the date.
We won ours on the boat ride in The Land on 10/26. So did all the other families on the boat with us.
Dream FP's are given out at the CMs discretion.
Someone asked if they ever expire. They are good for that day only. However, if the ride is down that day and you are coming back the next, the CM's will most likely let you use them. This happened to us with Test Track. We went to use our Dream FPs but the ride was down for the entire day. We brought the passes with us the next day and asked at the information booth if we could still use it since the ride was down the day before. We were told yes and to let the CMs know when we get there. One problem though, we hit TT first thing in the morning and there were no lines so we didn't need the FP afterall.