To caramelize something is to sauté it in a heavy skillet over a moderate heat until it’s natural sugars “caramelize” and turn brown.  This intensifies the flavor and is a good method to use when more bang for your buck.  Onions are often caramelized before adding to a dish to develop their full flavor.  Meat scraps and bones, and vegetables are often caramelized before using to make stocks and broths.  You may add oil or not, depending on what it is you are caramelizing.  The item may be sautéed to any degree from a golden brown to a deep mahogany color, depending on the application and the flavor you are looking for.

Place the material to be caramelized should be placed in a skillet and cooked gradually, over a medium-low heat until the desired degree of caramelization is achieved.  Do not try to hurry the process.  You will only scorch your item and create a scorched flavor.  

The term is also used to describe the process of melting and browning the sugar placed on top of some desserts, like Créme Brûlée.  Traditionally this was done under a broiler or salamander.  Now it is usually done with a small blowtorch.