The most aggressive ATV mud tires are designed primarily for mud riding only.  Extremely aggressive tires have the deepest of lugs for superior traction.  Their lugs are also spaced further apart from other tires, which allows them to clean out and perform better.  Some mud tires have lateral tread bars that go across the tire, which make for excellent snow tires as well.  

Aggressive ATV tires have great traction in the mud, but are not recommended for trail riding.  They will ride rougher and wear out quicker when ridden on hard surfaces.  These tires are also heavier than their less aggressive counterparts, which in turn make handling more difficult and can rob power from your machine.  The bottom line is aggressive mud tires make traction in the mud the number one priority!