a vowel can be looked at two ways: phonetically (vocalic) and phonologically (vocoid). Phonetically, a vowel is a sound that can be produced without a complete closure of the mouth (or cause friction). There are three different ways you can classify vowels phonetically. They are by nasality, position of the lips, and vowel height. Nasality refers to air also leaving the nose when the sound is produced. Position of the lips refers to if the lips are rounded, spread, or neutral when the vowel is produced. Vowel height refers to the position of the tongue when the vowel is produced. From a phonological point, a vowel is the center of a syllable. There are also glides, which involve the use of a vowel with other consonants that have vowel like qualities in order to make certain types of vowel like sounds.
Crystal, David. A Dictionary of Linguistics and Phonetics. The language library. Oxford, UK: Blackwell, 1997.