"Thick syrup" refers to a sticky, viscous liquid that has a high concentration of sugar or other sweeteners and is thicker than a regular liquid. Full definition
Add milk 1 Tbsp at a time and blend with fork until the glaze has the consistency of thick syrup. (sunnysideupsd.com)
Lower heat and simmer about ten minutes, or longer to get a slightly thicker syrup. (connoisseurusveg.com)
Edit: I reduced the amount of water in the recipe from 2 cups to 1 cup to cut down on the cooking time so that you get thicker syrup much more quickly. (strawberriesforsupper.com)