In order for a person to cross a room, that person must first cross the halfway point of the room. In order to reach the halfway point, the person must first reach the midpoint between the origin of the walk and the halfway point. And to reach halfway to the halfway point, the person must cross the halfway to the halfway to the halfway point.
Zeno argued that the process could be continued forever. The gist of the argument is that in order to reach the other side of the room, an infinite number of points must be crossed. And logic tells us that an infinite number of points cannot be crossed in a finite period of time. Therefore, it is impossible to cross a room.
QED.