The word blanch refers to a cooking technique in which food is briefly immersed in boiling water or fat.
Blanching vegetables softens them just enough so that they can then be quickly cooked over high heat, such as in a stir fry, where a short time in the pan wouldn't be enough to soften them, but cooking them longer would tend to overcook the other items in the pan.
Blanching is also a good technique to use for vegetables that will be featured in salads, so that they're softened just enough so that you can eat them more or less raw, but they won't be excessively difficult to chew.
Think carrots or broccoli here.
Vegetables such as green beans are often blanched in order to enhance their natural green color, as well as softening them. You'd want to blanch the green beans before using them in a Niçoise salad, for example.
Now, remember that "cooking" is mainly about getting something hot. Thus, as long as something is hot, it's cooking. All the molecular and other changes that result from this are happening: vegetable fibers soften, pigments change color and so on. And because vegetables are delicate, cooking them for two minutes instead of one can turn them limp, soggy and drab.
Therefore, blanched vegetables are typically plunged into an ice water bath afterward to halt the cooking process. This is called "shocking" the veggies. As soon as they're cool, drain them and set them aside. Leaving cooked veggies in the ice bath for too long will turn them soggy.
Ice water works best because it cools quickly.
Even a few cubes from your ice tray will make a difference. But use what you have. If all you have is cold tap water, then use that. It helps to run the tap for a few seconds until the water runs cooler. And do be sure to drain the veggies completely after shocking them.
Another use for blanching is to help loosen the skins on tomatoes and other foods.
If you make your own marzipan, you need to blanch the almonds to remove their skins. Also, when preparing white stocks such as chicken or veal stock, the bones are blanched beforehand in order to rid them of impurities.
When making french fries, the cut potatoes are often blanched in medium-heat oil and then cooled before frying them a second time at a higher temperature.