Thirds (and their inversion, sixths) are "imperfect consonances," which means they reside in a middle ground between dissonances (seconds, tritones, and sevenths) and perfect consonances (perfect fourths, perfect fifths, unisons, and octaves). Their middling level of consonance makes them usually preferable, especially in two-note harmony, to dissonances and perfect consonances, the reason being that imperfect consonances are neither harsh like dissonances nor excessively peaceful-sounding like perfect consonances. They have just the right level of "spiciness" to keep the music flowing smoothly. Of course, a good composer doesn't use them exclusively (particularly not when writing for 3 or more voices, where it becomes difficult to avoid using perfect consonances frequently)--just preferentially.