If you sync them, your flight logs will be uploaded to DJI's servers. That'll allow you to sync again later and pull them back down (or down to another device). If you don't need your flight logs, then it's okay to just delete them.
Some people like to review them after flying to see the recorded data. Perhaps they ran into a problem during the flight and want to see if the flight logs explain what happened. Other people use the flight logs to help locate lost Phantoms.