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.

Thanks for this, I'm planning on watching Bram's talk but haven't had the time just yet. It's definitely an interesting idea, so I'm eager to see how it plays out.

See the 'how it works' section for a brief description of Burstcoin's proof-of-capacity mechanism [1].

[1] https://bitcointalk.org/index.php?topic=731923.0

Yeah, same. Competing with Bitcoin is a tall order, but Bram is a pretty smart guy so there's definitely a lot of potential here. Thanks to dpiers for the description below, too!