Actual infinity, unlike potential infinity, is one interpretation of infinity where there is an end, of which we have no idea, say counting numbers (1,2,3,4,... it keeps going).
I have read about Cantor's ideas of countable and uncountable sets and his take on actual infinity.
My question is, and please correct me if I'm mistaken in my understanding, is whether a real interval (like (2,3)) an example of actual infinity. It clearly has a starting point and an end point. But, it also has infinitely many points with in it.
The point of potential infinity is that it is only used as a reservoir for more stuff (numbers, points, functions, whatever) and that it will never end.
Actual infinity, in contrast, is when you have an actual mathematical object which is infinite.
People who reject actual infinity, but accept potential infinity, will tell you that the collection of all natural numbers is not an actual mathematical object. Sure, there are infinitely many of them, but the collection as a whole is not a concrete object.
On the other hand, in modern mathematics, almost any reasonable foundations of mathematics will have a statement which says that the collection of all natural numbers is an object (in the case of set theory, this is the Axiom of Infinity, for example).
The interval $(0,1)$ is an actual infinity, yes, in that it is a concrete object and it is infinite. But so is $\Bbb N$, the collection of natural numbers.