In the Intake Report, you can adjust the daily intake of prisoners, i.e. how many and what kind of incoming prisoners there will be every day at 8 am. You can set up a total number (any number between 0 and all available) and the ratio of the different risk categories.
The ratio sliders affect which prisoners will be coming next from the pool, but they also affect which categories of prisoners will be added to your pool each day. Any prisoners not accepted will accumulate in a pool, and can be brought in at a later date, e.g. using the "All" option.
You receive a one-off payment for each incoming inmate depending on his category ($300 for minimum security, $500 for medium, $1,000 for maximum security). After this, every prisoner will generate a $150 prisoner grants payment every day.
Death Row intake is much slower than for the other categories, and there won't be Death Row prisoners available every day. Also, you won't be able to accept any Death Row prisoners until your prison has cells designated for them via sectors setting in Deployment view.
Note that the intake setting will not be decreased automatically, even if your prison's capacity of prisoners as displayed in the Top Info Bar is reached. You will have to manually stop the intake if you don't want to receive further prisoners. When you start a new sandbox game, intake will be set to "All", meaning that if you don't change the settings, your first prisoners will arrive after 24 hours, even though you might not have built any cells until then.