Atopic dermatitis is a condition of the skin caused by an allergy to something in the enviroenment with which one has come into contact. It is sometimes called "hives", and can (in the worst cases), precede a full-blown allergic reaction with shutting off of the throat and suffocation. It rarely gets that far, however. In the usual case, the person takes a medication or eats a food that they have become allergic to. They may not even know that they are allergic to it, or that they have ever come into contact with it. Shellfish are a notorious cause of hives. So are some nuts (e.g. peanuts). Penicillin is the most common of the drugs that can cause atopic dermatitis, and it can easily lead to the death scenario mentioned above. There is even a condition where exposure to sunlight causes atopic dermatitis!!!
What does it look like? It's usually started by itching on the skin, and then the person will look at the skin, and notice that it's red, blotchy, sometimes raised above the normal skin (Like red bumps on the skin, starting about 1 cm. in diameter, and relatively quickly coalescing to become one generalized red raised rash. It usually starts on the trunk, but spreads to the extremities within a day or two, sometimes within minutes. The quicker it spreads, the worse it probably will be.
Treatment depends on the extent and rapidity of onset. It may be aborted by the simple administration of an antihistamine (e.g. Benadryl) This can be taken as a pill (Over the Counter in the US), but a Dr. will usually give an injection for quicker relief. However, if the dermatitis is severe, the Dr. may prescribe steroids, at varying doses, or even epinephrine (adrenalin) if the condition is very severe.
In essence, it's redness and swelling of the skin, due to contact with an allergin (something someone's allergic to.)
That's the simple answer.
(It's also completely different from eczema.)