Turbo originally (in the early 1900s) was a prefix indicating that a turbine was somehow involved (turbofan, turbojet engine, turbocharger).
It later became shorthand for turbocharger, which I will not say any more about -- mister_clean and Bobby_Reb have covered that in excellent detail.
Due in large part to the fact that turbocharged cars are faster, and therefore insanely cooler, turbo has recently taken on the meaning of hyper-fast, uber-strong, or just plain super. At this point, I think that this usage can be safely classified as slang (or maybe as a buzzword).
The main use of turbo as an all-purpose intensifier seems to be in computer and Internet related subjects. We have Turbo Pascal, Turbotax, Turbo Star, Turbo Surfer, Turbo Squid, Turbolinux, TurboPower Software, and any number of others, including the rather mysterious turbo key on many keyboards. Of course, it's not limited to cyberstuff. There's also Turbo swimwear, the Hoover Turbopower vacuum cleaner, TurboRead Speed Reading, Wendy's Turbo Spicy Chicken Sandwich, Gillette's Mach 3 Turbo Razor, Turbo Truffles, The Turbo Nightclub, the Turbo Carver, Turbo Kayak and Canoe Paddles, and many others.
Probably connected to this trend, turbo is a slang term for marijuana laced with crack (AKA primo).
Definitely connected to this trend, the Mighty Morphin Power Rangers came out with Turbo: A Power Rangers Movie in 1997.