Don't be offended, but this question has been asked about 1000000000000000000000000000000 times before... there are hundreds of threads on this topic alone on bitog, go read them.
But yes there are benefits.
Synthetics (generally) provide better cold protection and hot protection as they break down less in the heat and don't thicken up as much when cold, they also cling to parts better.
Generally they are better at keeping engines clean, if you would change it at 3000 miles you would be better off with a conventional, even though most conventional oils nowadays can go over 5000 or 6000 miles given normal driving conditions, the 3000 mile rule is VERY outdated by now.
Synthetics were originally invented for Jet engines because they would withstand the heat unlike a conventional which would be absolutely turned to water by the heat, but they also found out later that synthetic base stocks provided cleaner engines.
There are also multiple types of basestocks like PAO, Esters and many more.
There are many other advantages and disadvantages but i hope you understand that the question you asked is a VERY broad question that would require a lot of writing to fully explain.
Although i've been on this board for less than a year i've learned a ton just from reading old threads.