A qualitative trait is a trait that can be described as a category.  For example, black or red coat color, horned or polled, coat color dilution are all qualitative traits.  Qualitative traits are frequently controlled by one or just a few genes meaning they are simply-inherited traits.  Conversely, quantitive traits are traits with phenotypes that can be measured numerically. These are traits like weaning weight and dry matter intake.  Usually, quantitative traits are polygenic meaning they are controlled by many genes and gene interactions. Some traits called threshold traits, are polygenic but expressed in categories - pregnant/open and occurrence of dystocia for example.  

Qualitative traits often (not always) have DNA tests for the genes of influence and breeders can use a Punnett square to determine the likelihood of different calves from a certain mating.  Quantitive traits typically require EPDs to make progress in genetic selection in those traits.