synthetic oils are more expensive then regular mineral oils for two reasons: the base fluids used in synthetic oils are subjected to longer and more complicated processing then standard base oils and that makes them more expensive, the other reason is marketing: buying something that is "newer and better" always comes at a premium...
from a pure technical point of view the synthetic products are "better" in a number of areas: better cold flow properties, so after a cold start all the engine parts that need oil are served sooner. They also can withstand high temperatures better, which means that they do not deteriorate (oxidize) as fast as standard oils, which means they can be used longer or can be used in engines that have parts that run at very high temperatures where standard oils fail to offer the protection needed. Another notable difference is that because synthetic oils usually contain less of the complex molecules that are used to modify the viscosity-temperature characteristics (viscosity index improvers) they are not as prone to temporarily loose part of their viscosity in high temperature high shear situations as can occur in the valve train areas of modern engines. Because they are less susceptible to temporary viscosity loss they can also be thinner, which can make a small contribution to lowering fuel consumption, especially when the engine is used for commuting traffic.
for a number of modern cars with extended oil intervals use of these new quality oils is a absolute necessity - standard oils do not meet the quality requirements for these designs.with other designs both synthetic and standard oils may be used - often with a notable difference in suggested oil change intervals.
thus, underlying the hyped marketing is a strong backing of relevant testing and specifications - these oils would not have been brought to the market if their was no technical need for their use.