The concept: To go anywhere, you must go halfway first, and then you must go half of the remaining distance, and half of the remaining distance, and so forth to infinity: Thus, motion is impossible.
The Puzzlin’ Part explained:
Attributed to ancient Greek philosopher Zeno, this proof was supposedly created as a proof that the universe is singular and that change, including motion, is impossible (as posited by Zeno’s teacher, Parmenides).
People have intuitively rejected this paradox for years. Makes sense, as motion is existent.
From a mathematical perspective, the solution — formalized in the 19th century — is to accept that one-half plus one-quarter plus one-eighth plus one-sixteenth and so on … adds up to one. $${1\over 2}+{1\over 4}+{1\over 8}+{1\over 16}+…=1$$This is similar to saying that 0.999… equals 1. Fancy mathematicians may call this by a fancy-schmancy name of convergence.
But this theoretical solution doesn’t actually answer how an object can reach its destination. The most accepted solution is that Zeno’s initial assumption that time can be split into infinite pieces, which is believed to not be possible.
The “true” solution to the paradox is more complex and still murky, relying on 20th-century theories about matter, time, and space not being infinitely divisible. If reading about that is your cup of tea, then here is a good resource.