Regular oil is refined from petroleum, meaning that its producers remove the components they don't like. Synthetic oil is made by combining base stocks of pure chemicals, so it contains very little or no contaminants.
Because it does not contain contaminants like paraffin wax and loose carbon molecules, synthetic oil is all but incapable of producing engine sludge.
Synthetic's cost is largely off-set by the fact that it usually lasts two to three times longer than regular oil under the same conditions.
Because synthetic oil is "slipperier" (has better lubricity) than conventional oil, you can use a lighter weight oil that decreases internal engine resistance (parasitic drag). Reduced parasitic drag equals more horsepower, torque and better fuel economy.
"Full Synthetic" oil only contains about 5 to 8 percent of actual synthetic base stock; the rest is machine-grade mineral oil. A quart of truly synthetic oil like Pennzane would run you about $400, which is why it's only used in aerospace and precision machine applications.
Even though synthetic oil costs two to three times more than regular dino-juice, it's manufacturer's claim that its benefits outweigh the cost. That assertion seems borne out by independent testing and customers alike.