Sure, we could get technical, and think about how the guitar pickups are used to capture the vibration from its strings (usually steel-cored) and convert it to an electric current. Such current is then modeled and altered through speakers and instrument amplifiers; there are several possible effects that can be applied to the audio signal that originates from the vibration of the guitar strings: reberbs, distortion, assorted gimmicks. But that's just the technical side of it, and it barely explains the unique sensations that can be offered by a good electric guitar.
Usually, electric guitars have six metallic strings although there are certain variants used in specific musical styles with seven or even a dozen strings (six pairs). This kind of guitar is used in all kinds of musical styles, from jazz, to metal, pop... and of course Rock'n'Roll music. Actually, the origins of the electric guitar can be traced back to the 1930s Swing-era Jazz movement, when guitarists started experimenting with steel pickups adapted to their hollow-bodied instruments, as a way to get a louder, more substantial sound than what would be possible from a regular guitar. The first commercial electric guitars came up in the mid 1940s, and by then a solid-body was already in use thus introducing the much familiar look that's now typically associated with electric guitars.
With over 8 decades of development, the electric guitar and music from guitars is getting progressively more sophisticated. Nowadays there are thousands of models available, from a number of manufacturers; electric guitars come in all kinds of shapes and sizes some reminiscent of the regular acoustic guitar, and some drastically different from the traditional instrument. Regardless, there's a number of features which are invariably present in practically every electric guitars: the headstock, neck, body and strings. The headstock includes the machine heads, truss rod (may not be used in all models), string guide and nut; this section is used for tuning and holding/adjusting the strings. The neck serves the function of supporting the strings, and it's comprised of a fretboard, the inlay fret markers, the actual frets and a neck joint. The body of the guitar is comprised of several mechanisms including the pickups (neck and bridge), saddles, tuners, pickup switch, control knobs (tone and volume), output connector and strap buttons sometimes others, in more sophisticated models. Finally, the strings are usual divided in brass and treble variants.
The body of the guitar is usually made of wood; different types of woods are used by different manufacturers, and there is ongoing debate concerning which is best. Typical woods include maple, mahogany, swamp ash and alder for quality guitars, and plywood or pine for cheaper, less durable guitars. While the type of wood used in the solid body of an electric guitar will noticeably affect the sound it produces, the quality of the sound is most affected by the pickups which convert the vibration of the strings into an electrical signal, as well as the amplifier that's used to shape and model such signal. We could go on and on dissecting the technical aspects of electric guitars, and yet never get close to that which makes that music unique: it's soul. That's something that can be clearly felt and experienced by players and listeners alike, but which all the while can hardly be put into words. Enjoy the electric guitar music loops!