In cooking, “sautéing” means quickly cooking chopped ingredients in a skillet, sauté pan, or wok with very little fat over high heat, stirring or tossing them so they “sauté” and brown evenly.
The goal is to sear the outside (caramelization) while keeping the inside tender; this concentrates the juices and brings out the flavors without prolonged cooking.
Example: "Sauté the mushrooms in olive oil."
Meaning: Pour the mushrooms into a very hot skillet over high heat with a little olive oil, and cook them fairly quickly, stirring regularly, so that they brown on the outside.
Remarks: Most of the time, we use a well-heated skillet and oil or clarified butter to allow the temperature to rise quickly.