Stirring was the act of moving food or drink around in its container with an utensil, for example a spoon.
In 2371, James T. Kirk asked Jean-Luc Picard to stir the eggs for him while in the Nexus. (Star Trek Generations)
In 2372, Joseph Sisko reminded Nathan to stir the gumbo. (DS9: "Homefront")
In 2375, Julian Bashir, while playing his Julian Bashir, Secret Agent holoprogram, ordered a vodka martini, stirred, not shaken. (DS9: "Badda-Bing, Badda-Bang")