Zeno, a follower of Parmenides, reasoned that any unit of space or time is infinitely divisible or not. If they be infinitely divisible, then how does an infinite plurality of parts combine into a finite whole? And if these units are not infinitely divisible, then calculus wouldn't work because $n$ couldn't tend to infinity.
Another way to think about it is a flying arrow must first travel half way to the target from where it begins ( the first task), then travel half way to the target from where it is now (the second task), then travel half way to the target (third task), etc... What you get is this...
$$\begin{array}{l} {d_{Traveled}} = \frac{1}{2}d + \frac{1}{4}d + \frac{1}{8}d + \frac{1}{{16}}d + ...\\ \\ {d_{Traveled}} = d\left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + ...} \right)\\ \\ {d_{Traveled}} = d\left( {\frac{1}{\infty }} \right) = 0 \end{array} % MathType!MTEF!2!1!+- % faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGceaqabeaacaWGKbWaaSbaaSqaaiaadsfaca % WGYbGaamyyaiaadAhacaWGLbGaamiBaiaadwgacaWGKbaabeaakiab % g2da9maalaaabaGaaGymaaqaaiaaikdaaaGaamizaiabgUcaRmaala % aabaGaaGymaaqaaiaaisdaaaGaamizaiabgUcaRmaalaaabaGaaGym % aaqaaiaaiIdaaaGaamizaiabgUcaRmaalaaabaGaaGymaaqaaiaaig % dacaaI2aaaaiaadsgacqGHRaWkcaGGUaGaaiOlaiaac6caaeaaaeaa % caWGKbWaaSbaaSqaaiaadsfacaWGYbGaamyyaiaadAhacaWGLbGaam % iBaiaadwgacaWGKbaabeaakiabg2da9iaadsgadaqadaqaamaalaaa % baGaaGymaaqaaiaaikdaaaGaey4kaSYaaSaaaeaacaaIXaaabaGaaG % inaaaacqGHRaWkdaWcaaqaaiaaigdaaeaacaaI4aaaaiabgUcaRmaa % laaabaGaaGymaaqaaiaaigdacaaI2aaaaiabgUcaRiaac6cacaGGUa % GaaiOlaaGaayjkaiaawMcaaaqaaaqaaiaadsgadaWgaaWcbaGaamiv % aiaadkhacaWGHbGaamODaiaadwgacaWGSbGaamyzaiaadsgaaeqaaO % Gaeyypa0JaamizamaabmaabaWaaSaaaeaacaaIXaaabaGaeyOhIuka % aaGaayjkaiaawMcaaiabg2da9iaaicdaaaaa!7035! $$
But suppose we wish to calculate the area below a function between $a$ and $b$ say, the bars that compose this area consist of taking a reference point on the first bar $f(a)$, multiply it by $dx$, then using the slope $f'(a)$ as a guide, "jack up" the reference point onto the top of the next bar, multiply by $dx$, jack it up, multiply by $dx$, and repeat this until we reach the final bar (L.H.S.). The summation of all this yields the exact area.
So, it's like taking the line segment $ab$ and dividing each piece over and over again. Per division, the sizes of the pieces are half of what they were before, but there are twice as many of them as before; but as the number of divisions tends to infinity (n tends to infinity), they diminish to almost nothing such that when added back together, they still equal the length of the original line segment $ab$.
How does one understand and resolve Zeno's paradox?