Short Answer: It goes into a hole in the ground.

Details: A modern indoor toilet uses too much water to use in places where the water was pumped by hand so you have to "take it outside".

There will be a small separate building, variously called an "outhouse" (in N America), "privy", "bog", "dunny", "pit latrine", "little house".

Typically there is a hole dug in the ground and a shack with a seat is placed above it. When the hole fills up, you dig a new hole and drag the shack over to the new location.

As you can imagine, there is a health hazard. Waste from the pit toilet could contaminate the ground water, so you want to have it in a different direction from your water supply.

For late night or the elderly they could use a chamber pot, but in the morning it's going the same place.

I'm told that in Vermont some people would hang the toilet seat on a hook just inside the door of the main house in the winter so that it would not be as cold in the morning, but I cannot find sources for this.