Vowels are speech which are made on the most open stricture of approximation: there is a wide gap between the highest point of the tongue and the roof of the mouth. As a result, the configuration of the mouth is such that it is ideal to resonate, there is no audible friction.
Phonetically, vowels are classified in terms of the location of the constriction (front vs. back), the degree of opening (close vs. open) and whether there is lip rounding or not (rounded vs. unrounded). Vowels are typically represented on a vowel chart such as the one at the top of this page. There seems to be a natural relationship between the location of the constriction and lip rounding: front vowels are typically produced with spread lips, while the back vowels are typically rounded. This is well-illustrated by the total numbers of these vowels in the languages of the world.
Apart from these basic distinctions vowel can contrast in duration (short vs. long), their conformational aspect (oral vs. nasal). The vowels in some languages also contrast in voice quality (modal vs. creaky). The videos on this page only demonstrate some of the more basic distinctions.
The total number of vowels in the vowels systems of the world's languages varies considerably. The smallest systems consist of three vowels only, while some vowel systems may have 30 different vowels. The most common vowel system contains 5 vowels, i.e. i, e, a, o and u.