Question:  What is a matte finish paint?

Answer:  Matte refers to the sheen level of the paint.  Matte finish means a very flat finish with not very much sheen at all.  These finishes are typically not very washable so they shouldn't be used in high traffic areas or places where washability is a concern.

There are washable matte finishes but they typically cost more money than a regular flat or matte finish.  

Question:  What is an eggshell finish paint?

Answer:  Eggshell refers to the sheen level of the paint. Eggshell means that the paint is about as shiny as an egg's shell.  It is one step shinier than a flat paint, but duller than satin paint.

Eggshell paints look flat from a distance but display a slight sheen when viewed from an angle.  This sheen is great for bedrooms, dens, great rooms, etc.  

Eggshell paints are washable but not as washable as higher sheen paints such as satin or semi-gloss finishes.