One of the central elements of Aristotelian and Scholastic metaphysics is the distinction between two modes of being: act or actuality, and potency or potentiality. Act refers to a way a thing actually is, whereas potency refers to a way a thing is potentially. This distinction of modes of being is an important part of the necessary structure of a world in which there is change; in other words, if things did not exist in these two modes, things could not change.
Why not? I will explain drawing largely from Edward Feser's books, though I won't take the time to cite chapter and verse. I will give the broad idea.
Parmenides was an influential Greek philosopher who argued that change was an illusion because it was actually impossible. For Parmenides, there was a fundamental distinction: being and nonbeing; what is, and what isn't. Being is, whereas nonbeing isn't, and ex nihilo nihil fit -- from nothing, nothing can come to be. But change, Parmenides insists, would have to be a case of being coming from nonbeing. Consequently change is impossible.
Consider the case of a banana turning brown. At one moment in time (t1) the banana is yellow, and later on (at t2) it is brown. Now whence came the brownness? The whole structure of the banana at t1 was such that it wasn't brown. If anything about the banana could cause the brownness, it would have to have already been brown at t1. It wasn't already brown, however, and therefore it would seem the brownness came from nowhere at all. Since this can't be, change must consequently be an illusion.
It won't do, of course, to suppose that there is some underlying physical process taking place within the banana which accounts for its going from yellow to brown. This example is intentionally crude and undeveloped for the purpose of showing that it is universally applicable. At some point in that physical process, there would presumably have to be change. Parmenides' argument can be offered against any instance of change in the banana of no matter what sort, at no matter what interval of time in the banana's history.
The point of Parmenides' argument is this. If there is only actual being, then there cannot be any change. For a fully actualized being to lack a property or quality at one time and to gain it at another is for something to come from nothing. If there was any kind of causal relation between its actual properties and the property gained through change, it would already have had it, since those prior properties already existed within the object.
Now the Aristotelian does not deny the existence of change, but he sees the difficulty of the argument. The response is to grant that being cannot come from nonbeing, but to deny that all being is actual. There is also potential being -- there are the ways a thing is potentially, in addition to the ways it is actually. Change is a thing's potentiality being actualized, it is its potency being reduced to act.
The banana is actually yellow at t1 and actually brown at t2. But this change is a real phenomenon and not a case of being from nonbeing, because at t1 the banana is potentially brown even if not actually. The potential-brownness is a real aspect of the being of the banana, and it is actualized through whatever physical process. Being potential being is nevertheless being, there is no violation of the principle that ex nihilo nihil fit.
This distinction between actuality and potentiality, therefore, is a necessary part of any complete picture of the world. Apart from this real and not merely conceptual distinction of being, change could not really occur, since otherwise Parmenides' argument would succeed. The starting assumption of the Aristotelian, moreover, is that through our senses and our intuitive faculties, we are basically "in touch" with the world out there. Parmenides' argument supposes that our senses are not in contact with reality, that in fact they deceive us. In this way, the Aristotelian distinction is important to the practice of science, which presupposes we can come into contact with reality and genuinely know it through our senses. A part of that reality is change, for which the Aristotelian distinction is a necessary precondition.