Phonetics is the study of speech sounds. It is concerned with the actual nature of the sounds and their production, as opposed to phonology which operates at the level of sound systems.
The object of study of phonetics are called phones. Phones are actual speech sounds as uttered by human beings.
Of all the speech sounds that a human vocal tract can create, different languages vary considerably in the number of these sounds that they use. Languages can contain from 3 to 30 vowels and 5 to over 100 consonants (roughly, anyone know exact numbers?). The English language is pretty close to average, using 13 vowels and over 30 consonants. This differs from the lay definition based on the English writing system, where there are 21 consonants and 5 vowels (although sometimes y and w are included as vowels).
References: On-line phonetics course