What is the link between asthma and eczema?

Atopy (see below) Asthma, eczema, & allergies are "atopic" diseases. "atopy" is an inherited tendency for developing any of these diseases. That being said... If you already have one of these diseases or have a close blood-relative who does, you have a higher risk (than those who don't) of getting any atopic disease. Note: an increased risk does not mean you actually will get any or all of these diseases.
Allergy. Both eczema and asthma have allergy as possible etiology. They are "linked" by this common etiology.