Causality as a concept comes to us from the push. We push something and it moves. If we push a person, they react. Cry. Push back. Laugh.
We form an ordered pair of (push, move), (push, cry), (push, push back), (push, laugh).
In this case, more than one thing can happen from a push. In math we call this a relation.
If we can restrict this indeterminacy by adding more data to the push, then we can get a single output for a single input.
This gives us the function.
Thus ordered pairs and functions can be understood as soon as we begin to understand pushing and causality from pushing.