When you hear the organ sound in jazz, blues, gospel, rock and even country music, it's usually the sound of a Hammond, and more particularly, a vintage Hammond B-3 "tone wheel" amplified through a Leslie Speaker with rotating horn in a wood cabinet. There's nothing like that sound. Even digital samples don't quite measure up.
For the purist, it helps if the amplifiers in both the Hammond and the Leslie have vacuum tubes, rather than transistors or digital chips. It's the old-fashioned heat and distortion in the tubes that makes the character and warmth of the sound.
Before electricity, mechanical organs used to be comprised a lot of metal pipes (each shaped like the old metal boatswain's whistle) in incremental sizes from short lengths (for the higher pitches) to about 16 feet (for the lower bass notes). Some of the pipes were made of wood. Air was pumped through a particular pipe as a corresponding key on the organ keyboard was pressed. All these pipes and blowers required a lot of space-- sometimes a separate room. You can still see and hear "pipe organs" in older churches.
The Hammond organ was invented by clockmaker Laurens Hammond in 1934 and was originally sold to churches as a lower-cost alternative to the wind-driven pipe organ. The Hammond is a mechanical organ (as compared to transistor, solid-state and digital). There's a "tone wheel" which has a number of metal disks attached to a revolving metal shaft coming out of an electric motor. The tonewheel actually has to be oiled through a wick (cotton string). Magnets pick up the electric impulse produced by the revolving disks, which is converted into a signal to be amplified into sound. There are several additional mechanical parts which can change the sound, such as "draw bars."
In the 1950s, 1960s and 1970s it became a standard keyboard instrument for jazz, blues, gospel and rock music. Jimmy Smith is probably the originator and best known of jazz organists. Growing up in the early 1960s, my Dad had a couple of 33 rpm vinyl albums of Bill Doggett, who was more of a swing and blues organist. More recently, I had a chance to meet Joey De Francesco. There are lots of other super organists and I've heard a couple of them live.
A few years ago I saw and heard Ray Charles perform at the Paramount in Seattle. Of course he was great! The organist on stage had a Hammond and two Leslie speakers. That was a premier setup.