For those of you who dislike shaking your martinis, you can stir. Basically, you add your ingredients into an ice filled pitcher of some sort and stir. The goal here is to mix and chill your ingredients.
To move foods around with a spoon in a circular motion. Stirring is done to move foods when cooking. It is also used to cool foods after cooking. Most importantly, if a recipes calls for stirring to combine foods, such as a batter, before cooking, it usually means to gently mix just until well combined, as opposed to beating, which takes more strokes.