There is no centre, and it's not expanding into anything. A reasonable 2D analogy is the skin of an inflating balloon, in which points on its surface are all getting further apart but there is no centre of expansion, and no 'empty skin' that the points are expanding into.
In the case of the universe it's as if the skin is somehow powering its own expansion - the question is what that expansion rate is, and how has it varied over time?