Once you've reached Episode 2, you can automate your Businesses.
Automation requires a certain Character at a specific level and a certain amount of Cash. This varies Episode to Episode. You'll see some rotating arrows beside a Character. When it turns from grey to green you'll know you've met the requirements to automate that Business. You can always tap on the grey arrows to see what's required to automate that Business.
Once automated, Businesses will make Cash at the same rate as if you were playing!