The simplest definition of ethnomusicology that I have found is "the study of people making music" - attributed to Jeff Todd Titon, professor of ethnomusicology at Brown University.
Merriam-Webster's Collegiate Dictionary has this to say on the subject:
1 : the study of music that is outside the European art tradition
2 : the study of music in a sociocultural context
No. 1 seems today to be slightly outdated. The music of European cultures is not outside the scope of contemporary ethnomusicological research, although the early ethnomusicologists specifically excluded Western art and popular music. The definitions have been widened significantly, especially since the 1960s. (It should also be noted that, contrary to what seems to be popular belief in Western Europe, 'ethno' is not synonymous with 'Non-European', and even Western Europeans belong to a people or culture, which is, put simply, what 'ethno' means.)
The discipline was known as comparative musicology from the late 19th century until Jaap Kunst, a Dutch musicologist, introduced the term ethnomusicology in 1950 in a booklet called Musicologa. The new term was accepted and adopted quickly, and already in 1955, the first Society of Ethnomusicology was formed in the USA.
Ethnomusicology is the academic study of music of all types and from all cultures. It draws upon both musicology, which is the formal study of music, and upon anthropology, the study of cultures and peoples. In addition to studying the music "itself", ethnomusicology looks at the role of music in human life, analyzing the relationships between music and culture.