.. uses 'logic' to argue that an arrow in principle should never reach its target, since the remaining fractions of time can themselves be divided into small fractions, those then can be further subdivided, and so on ad infinitum. So, he tries to argue that there is an infinite amount of time left, and the path can never be completed. The paradox is that we know in reality that doesn't happen ..

this page puts it well -

What this actually does is to make all motion impossible, for before I can cover half the distance I must cover half of half the distance, and before I can do that I must cover half of half of half of the distance, and so on, so that in reality I can never move any distance at all, because doing so involves moving an infinite number of small intermediate distances first.

This is really sort of silly since we're actually talking about an infinite number of infinitely smaller fractions, and mathematically it's proved that adding all these up in principle will give you a whole number: 1, where 1 represents the total, completed path. So the arrow does hit the tree after all. (and Achilles wins ..)

Again, the page is probably clearer -

Now the resolution to Zeno's Paradox is easy. Obviously, it will take me some fixed time to cross half the distance to the other side of the room, say 2 seconds. How long will it take to cross half the remaining distance? Half as long – only 1 second. Covering half of the remaining distance (an eighth of the total) will take only half a second. And so one. And once I have covered all the infinitely many sub-distances and added up all the time it took to traverse them? Only 4 seconds, and here I am, on the other side of the room after all.

Maybe this example shows up some difference between Zeno's type of 'logical argument' (which might just be sophistry), and mathematcial proof.