When a product runs out, you decide what the customer sees: nothing, the product marked unavailable, or the product as normal, as if it were in stock.
Do not display in catalog — the product disappears from the listing. Anyone holding its direct link lands on a "not found" page.
Use it when you don't know whether you'll restock.
Show as unavailable — the default. The product still shows, but the buy button is replaced by Unavailable, and its page reads Out of stock.
Use it when you will restock. The customer sees you carry the item and comes back.
Show normally — the product shows and can be bought, as if it were in stock.
Use it when you make to order, or when you have the item on hand without it being entered in the system.
The rule only applies to products that have stock control enabled and that do not allow negative stock.
In other words: if a product is set to sell without stock, it stays purchasable in the catalogue under all three settings. This setting doesn't override that one.
Same logic, variant by variant. With Show normally, every enabled variant is available to choose. Under the other two options, only variants that still have a balance appear.
If all variants are at zero, the whole product follows the rule you picked.
A combo depends on the products inside it. If any item in the combo is out of stock, the combo counts as out of stock — unless you chose Show normally.
A hidden product doesn't show in search, doesn't show in its category and can't be found on Google. It comes back when you restock — but the time it spent hidden is time nobody knew you sell it.
When in doubt, Show as unavailable is usually the safer choice.