Conventional mineral motor oils are refined using crude oil for the base stock. Mineral oils contain impurities, such as nitrogen, resin, asphalt, wax, carbon, sulfur and aromatic residues. Refining removes most of these, but some remain to cause problems, especially under high stress and temperatures. Impurities, of course, can appear during combustion. Because synthetic oils are slipperier, friction is reduced.
Fuel economy is improved only a little.
The real economic payoff comes from a reduction in repairs. Longer intervals between oil changes are possible because synthetics resist oxidation, suffer less viscosity breakdown and decompose less into sludge. But don't overdo it. If the synthetic costs twice as much as mineral oil, extend the oil change interval by a factor of two. Filters should be changed at the normal recommended intervals.