"Decarb" means decarboxylation. It is the process of removing the carboxyl group by converting into water (H2O) and carbon dioxide (CO2). You do this by heating the marijuana. The suggested method is placing the bud on a piece of tin foil or a baking pan in the oven at 150 degrees (F) for roughly 15 minutes.
Depending on how much bud you are using and how "fresh" (or wet if it wasn't cured properly - or you are being stiffed by measures taken by shady distributors to add weight to the buds) it is, it may take longer. When done the bud should be dry and flake into a powder when you roll it between your thumb and forefinger.
We do this because marijuana, when harvested, contains mostly THCA, which is not psychoactive. However during the drying and curing process some of the THCA will decarb into THC (it removes the carboxylic group, COOH). THC is psychoactive. Most weed, even if cured well will still contain a lot of latent "bang", in any of the remaining unconverted THCA. When you smoke weed this process occurs when the flame comes into close proximity to the buds. When cooking, you want to make sure your bud is at its maximum potential potency.
And Yes, you can use the tincture in cooking. The THC should remain in the food, well the alcohol will evaporate.