NASA’s Curiosity Rover has landed on Mars. A lot of time an effort has gone in to scheduling what will be done there, when it will be done, how much time it will take, etc. The work there is done using specific local (Mars) solar time, and the Martian day is 24 hours and 39 minutes long. For the people doing experiments, that means their day shifts “later” by 39 minutes every day. But since we prefer a 24 hour day with 60 minute hours, they have special clocks that keep “martian time”.
One of the reasons why knowing the time on Earth and Mars is important is because planets rotate, both around the Sun and around their own axis. Satellites orbit at known rates too. So we know where Earth and Mars are in their orbits around the sun. We know where orbiting communications satellites are, and when they can be used to relay information. So with accurate clocks on both Earth and Mars, and a way to coordinate “Earth time” and “Mars Time” we know where and when to point radios so scientists can communicate with their experiments on Mars.
You can read more about this in an article from The Atlantic.