How do electronic organs make music?

Electronic organs typically use a few loudspeakers to produce sound waves that simulate those made by windblown pipes. In some models, digital recordings of a few real pipes are used as a basis for electrically producing the waveforms. When notes are played one at a time, some modern electronic organs copy the sounds of individual pipes with remarkable realism. However, when many notes are played simultaneously, the organ's speakers produce sounds that are the electrically combined mixture of multiple notes. The listeners hear something significantly different than they would hear if each note originated from its own organ pipe, or even its own loudspeaker. The electronic organ's electrical mixing of tones creates a sound that can be perceived even by those lacking a trained ear as somehow unnatural and lacking the fullness and beauty of individual, separate sounds blended in the ear.

How Do Pipe Organs Make Music?

A pipe organ consists of a vast array of real pipes which each make their own sound from their unique position in the room. Your ear hears a chorus of sounds originating from as many different locations as there are pipes playing. The chorus is further enriched by the reflected sounds that are unique to each pipe's physical location in the room. In fact, a pipe organ is usually custom designed, and each of its pipes "voiced", to maximize its performance within the acoustical environment of the room where it is located. Even untrained, casual listeners will be uplifted by the complexity of sounds from a real pipe organ just as one would prefer a live concert to a recording.

The difference between electronic organs and pipe organs is analagous to the difference of monophonic sounds compared to stereophonic sounds multiplied many, many times over.

See the difference too!

Of course, the visual difference between electronic organs and pipe organs makes an impact too. Electronic organs have little to offer aesthetically. In many churches, the physical majesty of the pipe organ is the cornerstone of sanctuary architecture.
(Also see Directory of Recently Rebuilt Pipe Organs in North America and more information to help you answer the question --- "Should We Save Our Church Pipe Organ?")

Also see Why is the Sound of a Pipe Organ Better?
And The Sound of Music: Electronics vs. Pipes