A guitar synth is a synth module whose input device is a guitar instead of a keyboard. To quote Norm Leet from Roland's UK website, "The most important part of a guitar synth system is the divided — or hexaphonic — pickup, which allows each string to be treated individually and for the attached synth to be able to detect finger vibrato and string bending."
At first these systems were farily sizable, taking up so much space that they had to be housed in specially designed guitars that were part of the entire synth system. Today's synth systems, however, are tiny things that can fit into pretty much any guitar.
Modern systems send the pitch information as MIDI to allow you to control external modules or keyboards. This also means that pitch information can be recorded by a MIDI sequencer.
GUITAR WORLD's TOP-10 GUITAR SYNTH SONGS...10. "Stranger In a Strange Land," Iron Maiden, Somewhere in Time, 1986
09. "Never Make You Cry," Eric Clapton, Behind the Sun, 1985
08. "Are You Going With Me?," Pat Metheny, Offramp, 1982
07. "Who's to Blame," Jimmy Page, Death Wish II, 1982
06. "Venus Isle," Eric Johnson, Venus Isle, 1996
05. "Discipline," King Crimson, Discipline, 1981
04. "Racing in A," Steve Hackett, Please Don't Touch, 1978
03. "Turbo Lover," Judas Priest, Turbo, 1986
02. "Don't Stand So Close to Me," The Police, Zenyattà Mondatta, 1980
01. "Ashes to Ashes," David Bowie, Scary Monsters (and Super Creeps), 1980