The damper is used to control the airflow into the firebox. By opening and closing the damper, you have some level of control regarding how fast and hot a fire burns. This keeps your house at optimal temperatures, and your wood consumption to a minimum.
When first lighting the fire, open the damper all the way. This allows maximum airflow into the firebox, helping the flames from your newspaper or starter log to burn sufficiently to set the wood alight.
When a good fire is established, you can then regulate the flames by adjusting the damper.