The first stage, and the most often overlooked, a burning log goes through is that of drying. A green log can be composed of up to 80 percent water. The wood's water content also determines how easily the log will be to burn. By the time a log reaches your fireplace, this ratio is more likely around 20 percent, but the water still has to go someplace. As the wood heats, the water boils and evaporates, turning into steam. As it changes to steam, it consumes energy in the process, keeping the wood cooler than it will be at later stages.
After most of the water has boiled off, the wood heats up again. With the water gone, it can now reach temperatures much higher than water's boiling point. Between 400 and 800 degrees Fahrenheit, the wood loses its shape. It also emits smoke. This smoke is composed primarily of VOCs, or volatile organic compounds in gas form. These compounds can burn and it is their consumption that produces the orange and yellow flames that we associate with a wood fire. After most of these compounds have been consumed, charcoal remains.
Charcoal is made mostly of carbon. Charcoal, like most fossil fuels, burns very well, but there is a drawback. The burning of charcoal leaves carbon monoxide as a byproduct. Carbon monoxide has no color or odor, but is toxic in high quantities. A charcoal fire will have a dull orange or red glow. This fire needs oxygen to maintain itself. This is why poking at the log helps the fire to flare up again. As new areas are exposed to the oxygen-rich air, the process continues more easily. This is also why a fire can be "suffocated" by simply covering it.
All three processes discussed above are taking place at the same time. You will still observe some smoke coming during the charcoal phase and even some moisture being emitted. This is because water that was at the center of the wood is still escaping, and some of the wood is still being turned into steam. Burning the log did not cause the matter that made it up to vanish. Most of the matter simply escaped into the air.