Cardinal vowels are a set of reference vowels used by phoneticians in describing the sounds of languages. They are classified depending on the position of the tongue relative to the roof of the mouth, how far forward or back is the highest point of the tongue, and the position of the lips (rounded or unrounded).
A cardinal vowel is a vowel sound produced when the tongue is in an extreme position, either front or back, high or low. The current system was systematised by Daniel Jones in the early 20th century, though the idea goes back to earlier phoneticians, notably Ellis and Bell.
Three of the cardinal vowels—[i], [ɑ] and [u]—have articulatory definitions. The vowel [i] is produced with the tongue as far forward and as high in the mouth as is possible (without producing friction), with spread lips. The vowel [u] is produced with the tongue as far back and as high in the mouth as is possible, with protruded lips. This sound can be approximated by adopting the posture to whistle a very low note, or to blow out a candle. And [ɑ] is produced with the tongue as low and as far back in the mouth as possible.
The other vowels are 'auditorily equidistant' between these three 'corner vowels', at four degrees of aperture or 'height': close (high tongue position), close-mid, open-mid, and open (low tongue position).
These degrees of aperture plus the front-back distinction define eight reference points on a mixture of articulatory and auditory criteria. These eight vowels are known as the eight 'primary cardinal vowels', and vowels like these are common in the world's languages.
The lip positions can be reversed with the lip position for the corresponding vowel on the opposite side of the front-back dimension, so that e.g. Cardinal 1 can be produced with rounding somewhat similar to that of Cardinal 8; these are known as 'secondary cardinal vowels'. Sounds such as these are claimed to be less common in the world's languages. Other vowel sounds are also recognised on the vowel chart of the International Phonetic Alphabet.