A Concept Mark is one where a particular idea is trying to be conveyed that is not directly tied to the product/service or the company name. Instead, it is a concept that is important to the business and is usually very identifable to the market in which the business targets.
Take the Haggerty Lure Logo for instance. A gamefish was chosen to represent the company. A fish isn't what the company sells of course, but it is what the company is all about: Fishing Lures.