Vowels in the English language are A, E, I, O, U, and sometimes Y. The different ways of pronouncing vowel sounds, singly or in combinations, allow the consonants of the English language to be connected into words.
"Cardinal vowels" are not a different set of vowels than those listed above. Instead, the cardinal vowel system is a way to think about how the different parts of the mouth and tongue are placed and used in order to make the sounds associated with different vowels. The cardinal vowel system considers the amount of open space inside the mouth (height), the placement toward the front or back close to the throat (backness), and the shape and placement of the lips (roundedness) when articulating any given vowel sound. See the placement chart provided on the link below for an illustration of the relationships between these factors.