Shredding is basically the act of playing an instrument very fast. Although the term is most commonly associated with the electric guitar, it can really be applied to any instrument, and any musician who plays their instrument at high speeds could be considered a shredder. "Shredder" is the term applied to one who shreds.

Techniques
Shredders use a wide variety of guitar techniques to play quickly. Some of them are:
-Speed picking: A faster form of alternate picking - this is basically where one will play a series of fast licks and pick every note.
-Legato: Essentially the use of "hammer-ons" and "pull-offs" to string together a series of notes smoothly and quickly.
-Tapping: Using your picking hand's fingers to hammer-on notes on the fretboard and pull of to lower notes being fretted by your other hand.
-Sweep picking: A technique used to play arpeggios, or broken-up chords. The pattern will generally have one note on each string, and rather than picking each individual note in the phrase, the pick will be moved downward (or upward) across all the strings being played, hitting every string just as your other hand frets the correct note on that string.
-String skipping: A technique where one will play a short lick or phrase on one string, then skip on or more strings and play a similar lick on another string. Example: skipping from the G to the high E, or the D to the B. The greater the distance between the strings, the more difficult it is to execute properly.

Guitars
Guitars used by shredders are usually manufactured by brands that make guitars suited to playing some form of heavy metal. However, the guitar used is based on the guitarist's preference. Some of the most well-known guitar manufacturing companies are Gibson, Fender, Ibanez, Schecter, Dean, ESP, Caparison, Steinberger, and PRS.

Guitarists
Some of the best (in my opinion) modern-day shredders are:
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Buckethead - Known for his extreme technical proficiency in nearly all of the mentioned techniques, but also for his varied and eclectic playing style.

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Jeff Loomis of Nevermore - Known for his smooth and accurate sweep picking and fast speed picking.

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Michael Angelo Batio - Like Buckethead, he is well known for his incredible technical ability in all mentioned techniques. He was voted the number one fastest shredder alive by Guitar World magazine.

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Michael Romeo of Symphony X - Known for his fast speed picking, accurate string skipping technique, and his frequent use of combining string skipping and tapping to play arpeggios.

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Paul Gilbert - Known for his fast speed picking and string skipping.

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Rusty Cooley, formerly of Outworld - Known for his technical proficiency in all mentioned techniques, but especially for his extremely fast speed picking.