Cost: The number of missions that NASA runs is limited by its budget. Communication with Earth is an expensive part of running a mission. If NASA can lower costs by needing less communication with Earth, more missions could be conducted.
Ability to deal with emergencies: Because radio waves only can travel at certain speeds, it can take a long time for communication to go from a spacecraft to Earth and back. If a failure takes place during a crucial part of the mission, it may take too long for Earth to hear about the failure and send commands for what to do. If a spacecraft can handle many emergencies on its own, there is a higher chance the mission will be successful.
Ability to explore remote regions: The further a spacecraft gets from Earth, the more difficult it is to communicate. There are some areas, like below the ice of Europa, Jupiter's moon, that communication with Earth would be impossible. If a spacecraft is autonomous it has the opportunity to explore these regions.
Why was Remote Agent chosen to go on DS1?
What is the New Millennium Program?
What is autonomy technology?
Why don't we just send astronauts on deep space trips?
What does it mean to be autonomous?
Why can't spacecraft explore under the ice of Europa using past technologies?
How does Remote Agent enable missions to take advantage of unexpected science opportunities?
How does Remote Agent help cut costs?
How does Remote Agent cause missions to be more reliable?