It is a very common skin condition of children and adults. Usual symptoms include excessively dry and sensitive skin, and rashes that erupt after excessive washing, during periods of low humidity, and in response to certain foods or other allergens.
Soap removes the protective oils from the skin, causing excessive drying and increased rash.
It is by the way perfectly OK to bathe just in water without soap at all. Gets 'em clean without removing the skin's protective oils. Reduce your child's bathing as much as you can when the skin is bad. There is now some evidence that at least for mild to moderate eczema, daily bathing with a moisturizing soap is not harmful at all. Since bathing is usually such a fun time with little kids, and involves touching and bonding as well as cleansing, I would really not be opposed to a daily bath unless the rash were really bad.