Blanching entails briefly cooking something and immediately cooling it to stop the cooking process. The most common form of blanching involves boiling vegetables in liquid, draining them, and then using an ice bath to stop the cooking process. This last process of introducing hot boiled vegetables to an ice water bath is known commonly as shocking.
Chef Pace describes the difficulty of properly timing the boiling process when blanching. This difficulty is due to the high variability of vegetables and the myriad intended uses associated with blanched items. The boiling times will vary widely depending on the size, maturity, and type of vegetable being used. Chef Pace recommends tasting the vegetables every 30 seconds to see if they are are properly cooked, and appropriate for their specific application.
The carrots in this video were prepared for crudités. Chef Pace explains that while crudités usually describes a raw preparation, a brief blanching will impart some added brightness and sweetness to the vegetables.
Chefs like to blanch vegetables because it preserves and enhances their pigment. Vegetables like broccoli, asparagus, and green beans are commonly blanched because it keeps them from browning and will allow them to remain bright green for much longer. If preparing large amounts to be stored, or used for "mise en place," this becomes an essential cooking strategy.