Heraclitus said, "You cannot step into the same river twice, for other waters are continually flowing on."
How does this statement help illustrate his belief that "all is change"?
Heraclitus is famous for his argument that change is constant; that everything in the world is always changing. The saying that you quote shows this perfectly because it illustrates how even things that seem constant to us are actually undergoing change.
When we look at a river, we see a single entity that has always been there and always will, seemingly, be there. Therefore, a river seems to be almost the epitome of something that does not change. But, as Heraclitus says, it really is not possible to say that the river remains the same. The river is constantly changing and is, in effect, not the same river.
If you step in a river, you are stepping in a specific bit of water. If you withdraw your foot and step in it again, you are stepping in a different bit of water. Moreover, just by stepping in the river, you have changed it. You have altered the course of the water a little bit. You have eroded the river bed a little bit. The river is always changing and therefore it is never the same.
We can look at human beings and societies in the same way. We may seem to be the same person today that we were last week, but we have been changed in some way by our experiences. Society has been changed by all the things that happen. Human life is like the river that seems to stay constant yet is actually continually changing.
According to Heraclitus, who reasoned that everything is always changing and that this fact is fundamental to the functioning of the universe, it is not possible to step in the "same river" twice because the river is ever-changing. Although we may look at this river and see that it looks, generally speaking, the same as it did the last time we stepped in it, it is, in fact, different. Setting aside any potential movement of the riverbed, rocks, branches, fish, and the like, the water itself is always going to be different between any one moment and any other moment. It may flow from the same source; it may taste the same and look the same and be the same temperature, but it is different water than the water we touched the last time. Because the water is always moving, the river is never the same, even if we perceive it as being the same.
Something similar can be said for many other things: individuals, communities, countries, planets, universes. Even if change is slow—so slow that we cannot perceive it with our naked eyes—it still exists, always.