Autotracking is an aim support technology which enables your ship computer to calculate the future location (calculated from it's current velocity and moving direction) of your targeted enemy and fires your guns to this location. If you have beam weapons installed they are fired directly to the enemy.
Limitations and requirements
FIXME radar type + cone
How to obtain autotracking capability
Head to your local weapons dealer or upgrade shop and purchase [Weapons]->[Mount enhancements]->[Autotracking]. Then select a weapon slot (hardpoint, mountpoint) that doesn't have autotracking yet and confirm it.
Auotracking is not cheap, but worth it.