A simple syrup is truly simple -- just sugar dissolved in boiling water. The water-sugar ratio varies, but the standard is two parts water to one part sugar. 

Simple syrup is a bartender's staple; it's easier to swirl in a liquid than it is to add sugar directly, because the granules don't need to dissolve. Simple syrup is also handy to have on hand to sweeten iced tea or coffee. The syrup will keep almost indefinitely if stored in a tightly sealed bottle in the fridge. 

Simple syrups are used to soak cakes, poach fruit, sweeten frostings and make candy. You can flavor the syrup by adding any number of other ingredients -- ginger, orange or lemon zest, mint, basil, rosemary, lavender. Just put them in once the water boils right before adding the sugar, and strain them out before bottling.