Schemes vary on certain details, but the gist on PoC is that you precompute answers to puzzles that take up a bunch of space on a disk and miners search their disks for the best answers to mine a block. It's hard to compute the solutions during the window for the next block on the fly, so precomputation and storage are required. Everyone's answers are different because the miner's account identity is part of each solution. This approach seems strong from an efficiency, transaction rate, and decentralization standpoint, but it hasn't taken off, and I'm at a loss to why.
(Like I said, this space is full of scams, so it's hard to ask a question honestly without sounding like a shill. Maybe I shouldn't have bothered asking.)