Patina is a thin layer that variously forms (a small amount of surface rust, without pitting) on copper, bronze and similar metals.
The green patina that forms naturally on copper and bronze, sometimes called verdigris, usually consists of varying mixtures of copper chlorides, sulfides, sulfates and carbonates, depending upon environmental conditions such as sulfur-containing acid rain. In clean air rural environments, the patina is created by the slow chemical reaction of copper with carbon dioxide and water, producing a basic copper carbonate. In industrial and urban air environments containing sulfurous acid rain from coal-fired power plants or industrial processes, the final patina is primarily composed of sulphide or sulphate compounds. 
In layman’s terms, patina is a natural coating formed by the interaction of copper with water, air, and everything contained therein.
It’s not harmful to the copper itself, and in fact is part of the natural beauty of copper. It is possible to control the process somewhat – either by applying your own patina before mother nature does, or by applying a wax or sealant to inhibit the natural process. The easier option is to apply your own patina – once you’re done, you’re done. If you go the wax/sealant route, you’ll be re-applying and dealing with upkeep for the rest of your life. That’s another part of the beauty of patina (natural or contrived) – set it and forget it.
Inside your house is generally a much milder climate than the outdoors; therefore, patina on a copper countertop will not form as quickly as patina on copper gutters. The patina formed inside will take longer to form, and generally be less drastic. Regularly wiping your copper countertops with warm, soapy water will keep them from forming a thick patina layer – but they will most likely start to darken (again, this depends on many environmental factors, as well as what you spill on them).
My suggestion? Let them patina. If you can’t wait, have a patina applied before installation. But don’t seal them. You lose the anti-microbial benefits, and you’re inhibiting the natural process (and beauty) of copper. Oh, and adding to your to-do list.