Merrian Webster's Collegiate Dictionary defines cognitive as "of, relating to, being, or involving conscious intellectual activity (i.e. thinking, reasoning, or remembering)." I've always understood cognition as anything we are conscious of; it's the active processing of the stimuli around us. Cognition is a progressive thing, building upon itself over the years.
Take a newborn baby, for instance. They see the world around them, but they don't really know what they're seeing. They basically react to the following stimuli: hot, cold, hungry, tired, pain, and discomfort. We as parents talk to them and I'm sure they hear us and feel a certain sense of comfort, security, and love, but they haven't developed an outward recognition to us yet. As they grow older, nerve pathways are stimulated and develop, enabling them to recognize our touch, our looks, our voice. Soon, they begin to react to us through their body language, eventually interacting with us through their speech.
In contrast, metacognitive is defined as "awareness of one's own learning or thinking processes." It can best be explained as the sum total of everything a person has experienced and learned throughout their life. It is everything that's been absorbed into, processed by, and stored in our brain. A lot of it is subconscious, habitual, and conditioned; we don't really know how or why we know something; all we know is that we know it.
A good example would be a carpenter at work on a construction site. He needs to order lumber for the job so he rolls out the blueprints. The mathematical processes have been learned and stored in his brain, and knowing this, he gets to work to arrive at a final figure. This is the metacognitive process. If he runs across something he doesn't understand or know how to do, he takes the time to learn how to do it and understand it. This is the cognitive process.