There are many uses for mint syrup. It is really helpful when you are short on mint. I grow my own mint and in the winter and I'm usually nursing a pot along by the window. It doesn't grow very fast and when a Mint Julep party breaks out, having some mint syrup around can save the day.
I make mine using a spearmint tincture that I always have around. The recipe for the tincture is on this site.
This is for one tablespoon. Scale down for ad hoc mint syrup for a drink. You can scale up and make a pint of mint syrup to store in the refrigerator. Add a 1/2 ounce of 151 proof rum to preserve the pint of syrup and it will keep in the fridge for at least six months.