Webster1913, in his usual understated way, defines a drone as "that which gives out a grave or monotonous tone or dull sound." Mr. Webster could not have predicted that, only a few decades after he wrote this definition, a number of musicians would deliberately seek drones out, using "monotony" and "dullness" to create music that, paradoxically, ends up being neither monotonous nor dull.
Drones existed long before the experimental musicians of the 1960's and 1970's, of course. The bagpipe, the harmonium, the didgeridoo, and the Jew's harp are all very old instruments whose sound is dependent on a drone (in fact, the bagpipe's drone is created by a pipe that is actually called a "drone"). Whatever melodies any of these instruments may create will always be anchored by a low, constant -- but shifting -- buzz or hum.
Though a droning sound may originally have been perceived (at least in the West) as an accident of a given instrument's construction, certain modern musicians found drones attractive in and of themselves, and began to experiment with them. The electric guitar can very easily be persuaded to drone, and new electronic inventions such as the theremin could provide a different flavour of continuous noise. Hawkwind, Amon Düül, and Spacemen 3 were particularly well-known in the 1970's and 1980's for creating epic tracks powered by drones. Minimalist and post-minimalist artists like La Monte Young and Steve Reich played with subtler sounds.
From the 1980's to the 1990's, a whole slew of bands brought elements of drone into their music. Spiritualized, a Spacemen 3 splinter group, took their predecessors' work in even spacier and druggier directions; to this day they are considered by many to be the ultimate drone band. Later, My Bloody Valentine and The Jesus and Mary Chain would use guitar feedback as a kind of instrument, while math rock artists like Godspeed You Black Emperor!, Bardo Pond, and Mogwai would use their entire backing bands to contribute to a droney sound. Meanwhile, traditional instruments like the didgeridoo were appropriated by contemporary electronic artists such as Aphex Twin and Orbital. Even the bagpipes, long considered too dorky for rock and roll, were rediscovered and vindicated by bands like Test Dept..
Drone is a difficult concept to define, and people who like drone are quick to dissociate their favourite music from the tedious new age sludge in which someone simply holds a synthesizer key down with a finger for half an hour. On a mailing list dedicated to drone that was active some years ago, people spent more time arguing about what qualified as a "real" drone than actually talking about the music itself. Is krautrock drone? Is trance? Is shoegazer? Does anything repetitive or monotonous qualify as a drone? What is the best vocabulary to talk about the subtleties of a bagpipe's sigh or a blast of guitar feedback, anyway?
I can't answer these questions for you. All I can do by way of conclusion is repeat a famous quote by John Cage: "If something is boring for two minutes," he once said, "try it for four. If still boring, try it for eight, sixteen, thirty-two, and so on. Eventually one discovers that it's not boring at all but very interesting."
This writeup would have a lot more detail if only I could find a copy of the exhaustive droneon FAQ that was splashed all over the Web a few short years ago. If anyone has preserved it, I'd love to see it.
With thanks to Crux for artist suggestions.