A style of musical composition in which various more-or-less independent 'lines' occur simultaneously.
The independence is a result primarily of differing note start-times and durations, with the usual desideratum being that the harmonic relationships between simultaneous pitches be low-integer ratios (or close approximations of them).
Polyphony is unique to European art-music and other styles derived from it. The earliest documented examples are a particular type of polyphony called organum (Holy Roman Empire, c. 800 AD).
The full flowering of polyphonic style is most closely associated with music of the later medieval period and the Renaissance (c. 1200-1600), and of Johann Sebastian Bach (c. 1710-1750), with a resurgence in interest in it among European and American composers in the early-to-mid 1900s.