Var vs Let in for-loop?

Question

I was reading about closures in JavaScript when I came upon this problem:

for (var i = 0; i < 3; i++) {
  setTimeout(function () {
    console.log(i);
  }, 1000); // 1 second delay
}

My expected output is:

*loop finishes
0
1
2

Why is it:

*loop finishes
3
3
3

I don't understand how changing var to let fixes the problem, as they are both defined in the for-loop, so their scope should be the same.