The analogy I always use is a long straight flat desert highway. If you stand in the middle of it and look down its length, it appears to converge to a singularity in the distance. If you can see mileposts, you might even try to estimate how far away that singularity is.
But if you drive toward the singularity, you'll never run into it. It recedes before you. It is just a trick of perspective.
Basically all the talk of how crazy life will be after The Singularity is like trying to explain how crazy life would be on the other side of a rainbow. Fun, but not actually useful.