It is essentially a baked, typically vanilla flavored custard.
It is unique because they take the custard batter (eggs, cream, sugar and flavorings) and put it in little dishes/ramekins and instead of just baking it they put it in a shallow dish of water first. This transforms the oven into a little steam room where the creme brulees can luxuriate in their little spa and get firm but still creamy and rich. The extra moisture means that these little delicacies do not have a quiche or overly egg like texture, but one that is very smooth and creamy and will melt on your tongue a little. (softer than flan)
Once these gems are cooked, they are removed and given a thin dusting of sugar. They are then either broiled or blasted with a cooking grade blowtorch

(don't get scared now, lol) to caramelize the sugar on top. (The best part)
When it arrives to your table, you tap through this thin caramel colored layer of crisp sugar and get to the custard underneath.

The creaminess and crunchiness, the sweetness and the toasty flavor from the broiling are nice contrasts. I also like that creme brulees are usually not overly sweet.
Now, Disney has taken this basic recipe and created dozens of incarnation as we see from this thread! I have never had a creme brulee other than the vanilla or a homemade pumpkin one I made. I plan on trying a few of these when I go in December. They make me happy!
Hope that helped.