Synthetic oils bond to surfaces better and have a lower friction coefficient, so they are a better lubricant. Also, and probably more importantly, synthetic oils molecular structure doesn't break down due to age and thermal stress as conventional oils do. The main reason conventional oils must be changed every 3 months regardless of milage or every 3000 miles regardless of age, is due to molecular breakdown. Conventional oil will breakdown very quickly if overheated, synthetic will maintain lubrication at much higher temperatures. This means that synthetic is much more forgiving of infrequent oil changes, hot temperatures, and low oil conditions. I have seen more than one engine destroyed that might have been saved if synthetic oil had been used. Gas turbine engines require synthetic oil due to its superior properties in harsh conditions (high thermal stress, high rpm). This is also why many turbo charged engines should always use synthetic.
If you change your oil religiously every 3000, or 3 months (which ever is sooner). Never heat your engine past normal, and check your oil level every day or two, conventional is fine; it just doesn't have the extra margin that synthetic does.