A cocktail stick is a little stick that is used to stick pieces of food together. You know how sometimes grown-ups like to have fancy drinks with little pieces of fruit or olives in them? Well, sometimes these pieces are too small to hold onto with your fingers, so they use a little stick to pick them up and put them in their mouth.
It's kind of like when you play with little wooden blocks and you can stack them on top of each other to make a tower. With a cocktail stick, grown-ups can stack little pieces of food on top of each other to make a yummy snack. They can also use it to stir their drinks or to put a cherry on top of their ice cream sundae.
So, imagine a little wooden "sword" that's used for food instead of fighting dragons. That's what a cocktail stick is!