Adding fuel to a fire makes it grow larger. When examining the fire, I've seen three different messages, but it seems like there are more than three light levels. How much time does a single log add to the fire? Are there any effects besides duration to a larger fire?
Larger fires cast a wider radius of light, and offer more resistance against a later game creature which extinguishes fires. A single log adds 45 seconds to a campfire, and 90 seconds to a firepit. If it is raining, a firepit will consume fuel twice as fast. A more complete table of fuels can be found here.
While a Firepit is a controlled fire, a campfire is considered uncontrolled, and can jump to nearby flammable objects. The larger the fire is, the farther it can jump.