Basically stating that before you can go from one point to another, you must first reach the half-way stage between those two points. And before you can get to the half-way stage you need to reach the point half-way betwen your current point and the half-way point and so on, ad infinitum.
The problem with this line of thought, to my mind at least, is that while it is true you have to cross half the distance before all the distance, space is not discrete at a human scale - so you don't -have- to move in half-steps, which is presumed (but not stated) in the problem.
Another way to look at it: In classic math, a given distance can be divided into an infinite number of halves, since you can always divide a non-zero number by 2. This does not mean there is an infinite number of measurable units, it just means you can always divide by 2, because there is no limit on the number of ... numbers. This is, however, not the same as saying there is no limit on the number of motions needed to cross a distance.
In a way, it's a good show of the issue of quantum level events compared to macro-scale events - if you try to apply quanta to something like taking a 2 foot step, you get weirdness like this problem, because quanta don't apply on this scale. This, in it self, means we don't have a perfect mathematical understanding of reality.