"Sweated" vegetables are cooked covered, with a little fat, over very low heat so that they cook in their own juices without browning. A little salt and pepper is usually added, and a piece of parchment paper is pressed down on the vegetables before the pan is covered with its lid. Vegetables are often sweated for soup and for flavoring stuffings and dishes like quiche.
A similar technique, known as “stoving” in Scotland, is very successful with new potatoes and evenly cut pieces of Jerusalem artichoke. A light patching of golden brown is desirable.