A green kitchen is one designed to achieve two basic goals: First, do less harm to the environment than the typical kitchen, and second, actively help to clean up the environment when possible.
The latter goal is harder to achieve, but it's possible, mostly by way of green building materials such as bamboo. Bamboo butcher blocks are kinder to the environment than traditional wood, since bamboo grows back quickly after it's harvested. Build that bamboo butcher block into a recycled-material countertop, and you're doing all sorts of good. A countertop called IceStone actually uses recycled glass and concrete in its mix, materials that otherwise would end up in a landfill.
In kitchen design, green doesn't just mean recycling. Doing less harm to the environment also means cutting back on the use of and exposure to potentially harmful chemicals in our lives. You can find formaldehyde-free cooking cutting surfaces now. Formaldehyde is a chemical found in most homes (in cleaners and carpet, for instance). It's used in some wood products as a bonding ingredient, and it can produce an allergic reaction in certain people if they're overexposed to it [source: ATSDR].
Cooking green is also an overall approach to kitchen (and home) design -- it's not just product-specific. You can have your kitchen set up to be more energy efficient by connecting appliances so they benefit from one another's work. For instance, you can arrange it so the heat created by the compressor in your refrigerator is diverted to your dishwasher to heat the water.
Up next, another way to streamline the setup.