Dust mites are a type of tiny mite that feeds on the organic debris, or dust, in our homes. What we call "dust" is actually made of a mixture of hair, skin cells, plant pollen and other stuff that we and our pets shed every day, plus material that blows in from the outside. On a percentage basis skin flakes and dander from animals make up a large proportion of dust in the average household. Dust mites feed on this debris and usually go about their business pretty much unnoticed. Dust mites are light in color and tend to stay in undisturbed areas where dust accumulates.
Dust mite do not bite people or our pets and in fact don't have the type of mouthparts (jaws) that would allow them to bite even if they "wanted" too, nor do they burrow into skin in the way that scabies mites do. The main problem that dust mites cause is allergy. Dust mites are notorious for the allergens, substances that cause everything from a stuffy nose to full-blown asthma, that they excrete in their feces.
For more information about dust mites, dust mite allergies and protecting yourself from the allergens we've posted a series of articles at our 'Bugs site. The series start with "House Dust Mites and Dust Mite Allergens".