The word is from Greek, “poly” meaning many and “phony” meaning voice. This is as opposed to monophony — one voice. Originally, polyphony literally meant multiple people singing together. Over the course of musical history, the term has become more abstracted, referring to multiple “voices” played on any instrument. And usually, polyphony means that the different voices are all playing/singing independent lines.
So what exactly is a “voice” outside the context of a choir? If you have a wind or string ensemble, each instrument is a separate voice. Each plays a stream of notes, one at a time. In larger ensembles like orchestras, a number of instruments might play the same “voice” — for example, the viola section will act as a single entity, creating a single voice from unison.
You can also play music with multiple voices on a single instrument. That’s what’s happening in the Glenn Gould video above. Your ear perceives sequences of notes that are close in pitch and time as coming from a single “voice.” Notes that are widely separated in pitch and time sound like they come from different “voices.”
Consider the piano. If you play one melodic line with your left hand and a different one with your right, that’s two voices. It’s possible to play even more voices at once on the piano, as long as each line forms a coherent perceptual grouping. The same is true on the guitar, though keeping the voices independent is a lot harder than on a keyboard instrument. It’s even possible to simulate polyphony on a monophonic instrument — you can interleave the notes of a higher-pitched melody with the notes of a lower-pitched melody, and the ear will hear them as separate. Bach used this technique to great effect, for example in his famous cello suites. Check out this scholarly treatise on Bach’s single-instrument counterpoint by Stacey Davis.
Here’s a nice example from Wikipedia, showing the first few measures of the Allemande from Bach’s violin partita in B minor. One voice is in red, and the other is in blue.
Technically, any music with multiple voices is polyphonic, but classical music generally uses the word to refer to a specific technique called counterpoint. In counterpoint, each voice plays its own independent melodic line, and notes in the different lines coincide to produce chords. In counterpoint, there may not be any “foreground” or “background” line, just a mutual conversation. This makes the music very intellectually stimulating, though it can also be difficult to follow. Bach wrote huge amounts of beautiful counterpoint. By contrast, Mozart tended to use homophony, which organizes the voices in a way that’s more similar to modern pop songs: a complex foreground melody line accompanied by block chords and a simpler bassline.
You can hear polyphony in many styles of music other than western classical. In Dixieland jazz, the trumpet carries the melody while the clarinet and trombone improvise semi-contrapuntal lines around it.
Jazz from the swing era often has a soloist playing against a composed line or lines from the band. In bebop, the bass plays a continual countermelody consisting almost entirely of quarter notes, forming a kind of polyphony with whatever else is happening on top. And free jazz uses completely improvised polyphony among any number of musicians.