Anything contrapuntal has to do with counterpoint, which is a type of music that has two melodic lines played at the same time.
Many kinds of music (such as rock and country) are very simple, but others are more complex: such as contrapuntal tunes. Contrapuntal music involves counterpoint, in which more than one musical line plays at the same time. The lines are independent but related harmonically: creating that relationship isn’t easy. A contrapuntal composer therefore must be very skilled, because contrapuntal music has a lot of balls in the air — or rather, notes. You can also call contrapuntal music polyphonic.