Simple syrup, sometimes called bar syrup or sugar syrup (or gomme syrup to the Britishers*), is one part sugar and one part water. You can buy it at the liquor store, but it's super easy to make your own: mix one cup of sugar and one cup of water in a saucepan over low heat. Stir until all the sugar dissolves and the syrup is clear. Bottle the syrup (a funnel will come in handy here) and keep it in the fridge for up to a month.
*I just looked this up and it turns out that, although many people use "gomme syrup" to mean just plain simple syrup, real gomme syrup has a 2:1 sugar/water ratio and contains gum arabic, an emulsifier, to keep the sugar from crystallizing. Apparently it will give your old-school, booze-heavy drinks a beyond-incredible smooth texture. Future project? Mebbe. Read about it here.