My Lands: Black Gem Hunting

what determines how far a settler can travel?

The size of the world.

so I could send a group of settlers from one end of the map to the other?

Yes, you can. Though if you send them far away, it will take a long time to reach their destination. And maybe you don't even know what is there because it is too far to explore, and the mission may be a failure. So there is always a risk of wasting your time.

Explorers can only go as far as the science is researched right? So if you send a settler, you won't know the size without first exploring it right?

Yes, explorers have only a limited range. But you don't have to explore the cell where you want to build a new city. You can send a settler blindly, anywhere on the map. If the target cell is suitable for city foundation, a new city will be founded. If not, the settler will return unharmed, and then you can try it again somewhere else.

Would you want a settler to found a city without knowing what type and size it was? Maybe I'm confused on what settlers do.

Why not? Maybe you want a temporary city which you will destroy eventually, and its size doesn't matter.