It means that they can make their own schedule and decide when to work. It’s possible to work for someone else but be able to decide when you will work. For example, I get to set my own schedule when I do writing work. I have to finish the work by a specific date and time but it’s up to me how I spend my time until the deadline.

I interpret it as meaning a person works for themselves and does not have an employer/boss telling them when they have to work. For example most people work for someone else and must work, say, 9 to 5. However someone who teaches on iTalki from their home can “make their own hours” by choosing when to work and when not to.

hours refers to the time at work. ie. we need extra hours to finish this work. and make your own hours means what they have already told you.