You need a place for the metal to enter the empty space of the mold, and others for the air the metal is displacing to escape. The metal also contracts a bit as it cools and solidifies, and a good mold is designed such that the main filling sprue is where most of that happens, usually in the form of a giant dimple on top. These vents and filling holes, once filled with metal, leave behind the stem-like sprues on the solid casting....

But, what I described is more applicable to investment casting than die casting.

Die casting is actually a little more specific than just 'pour metal into mold,' but all of the above is largely still true. It's more like a glorified waffle iron process, where molten metal is poured into half of a mold, then another half (or, say, a third core between two sandwiched halves to cast something hollow) is pressed in, usually under some force, which forces the molten metal into both halves, and any excess volume 'squirts' out through the vent/sprue holes, leaving behind sprues and, where the mold halves meet, flat, usually razor-sharp flashing.