The phrase implies trust in someone's ability to handle things without guidance. Since he's a quick learner, his tutor decided to leave him to his own devices.
Pro Tip 2/3
Potential Neglect
Can suggest negligence if someone needs help but is left on their own. Ignored by the babysitter, the children were left to their own devices all day.
Pro Tip 3/3
Not Literal Devices
It's metaphorical and not about physical devices like phones or computers. During the exam, students were not allowed notes and were left to their own devices.