Zeno's paradox can be quite difficult to understand, because, as its title says; it's a paradox. Zeno imagined this paradox (among others) to support Parmenides' doctrine that motion is impossible, it is just an illusion. Let's take the most well known paradox, which is the race between Achilles and a tortoise.
Achilles and a tortoise are about to start a race. As Achilles is very fast, and the tortoise very slow, the athlete decides to start running when the tortoise is 100 yards ahead of him, to make the race fairer. But Achilles will never be able to catch up with the tortoise. Why? Common sense makes us think that if Achilles is faster than the tortoise, he's going to win the race. When Achilles has reached the point where the tortoise started, it's no longer there, the tortoise is a short distance ahead of him. But when Achilles run to the second point where the tortoise was, the tortoise is still ahead of him, and so on.
Why doesn't it work in real life then? Well, the answer is actually quite simple. Zeno considers that the distance between the tortoise and Achilles is infinite, and that we can divide it endlessly. However, in real life, we can measure the distance between the tortoise and Achilles, it is limited, that's why the athlete would win the race against the tortoise.