Comment by dpiers

My understanding is that your computer computes the answer to a difficult calculation ahead of time and stores the output up to a specified size (ex. 1GB worth of digits of pi) . Proof-of-Space asks you to respond with a segment of the output at a certain offset. The amount of time given to respond is less than the amount of time it would take to calculate the output, and so by replying you prove that you had it stored already.