In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice (monophony) or music with one dominant melodic voice accompanied by chords (homophony).
Within the context of the Western musical tradition, the term is usually used to refer to music of the late Middle Ages and Renaissance. Baroque forms such as the fugue, which might be called polyphonic, are usually described instead as contrapuntal. Also, as opposed to the species terminology of counterpoint, polyphony was generally either „pitch-against-pitch“ / „point-against-point“ or „sustained-pitch“ in one part with melismas of varying lengths in another (van der Werf, 1997). In all cases the conception was likely what Margaret Bent (1999) calls „dyadic counterpoint“, with each part being written generally against one other part, with all parts modified if needed in the end. This point-against-point conception is opposed to „successive composition“, where voices were written in an order with each new voice fitting into the whole so far constructed, which was previously assumed. (-> Wikipedia)
Here is a little collection of polyphonic singing all around the world.