So to cover the obvious case first - If your business is successful enough, you hire a CEO, employees, etc, and hand off daily operations to them. Of course, you as the owner are involved in the company still, but the majority of your time should be free to tackle other issues. Elon Musk is a good example of someone who has done this. He has multiple companies, working on different issues. Of course each company you start takes a significant up-front cost of your time. But the more successful the company comes, the more likely you are to be able to onboard employees who can give you back your time. Clearly, this is only possible once you have "made it big", and it's not really the type of business I am speaking about.
The other type of "autonomous" business is a SAAS business. The idea here is that you build a software service that generates revenue. This revenue should come in the form of monthly subscriptions to your service. If you can keep your costs down (i.e. do the work yourself, and don't hire full time employees), then once your system is stable, it should be able to generate income with relatively minor investments to your time. Obviously again with this case, a significant UPFRONT effort must be made to develop a system that provides enough value to customers, that they will pay for it.
I've been working on my business now for over 2 years. It's been a side project that has consumed a healthy majority of my spare time outside of my 9-5. I'm on track to break-even in revenue/costs in 3-4 months. Around that time frame, I also expect to be "feature complete" with version 1.0.
This should sustain at least a year, if not longer, of minimal time investment. Sure, I might need to fix a bug here or there, or investigate a connectivity issue or something that I simply can't 100% protect against... But the system has been developed from the ground up for long term stability, and reliability.
It's been running now for 2 years, and I've had basically no issues that I've needed to fix. It's been all feature development. By the end of this year I can pretty much guarantee I will be hands free, spending less than 3 hours a week, making more money than I spend.
That is the goal. Build something that can run (mostly) by itself, that generates more income than it costs to run.
p.s. Knowing myself, because I love what I do, I'll continue to work on it just for fun. But there's immense peace of mind knowing I don't have to.