Simple syrup is basically sugar dissolved in water in a ratio that can range from 1-to-1 (sugar to water) to 1-to-3. The lower the ratio of water to sugar, the sweeter the mixture will be. Simple syrup is useful for making beverages (including alcoholic drinks) sweeter without a grainy texture of sugar that might remain undisolved if the sugar were added in its granular form.
You can make simple syrup by bringing water and sugar to a rolling boil, then stirring and cooking the combination (at a boil in some recipes for 1 minute, at a lower temperature in others for 2-3 minutes) until the sugar is completely dissolved, then letting the mixture come to room temperature.
simple syrup at a rolling boil
simple syrup cooling
Simple syrup can be kept in a closed container in the refrigerator for several weeks.