Proof-of-burn isn't a new concept, but the Koinos implementation is novel. Basically, you burn (destroy) some of your Koin and the blockchain gives you a "miner NFT". This is a virtual representation of what happens with Proof-of-work. Instead of trading dollars for hardware and electricity, you trade Koin for NFTs.
You can think of it kind of like buying bonds. You're trading money now for a promise of more money in the future. In exchange for securing the network, you'll be rewarded with new money created through inflation. Your return on investment is guaranteed, but the turnaround time is variable. If the network needs more securing, you'll get your money faster. If there's already a lot of people securing the network, it will take longer.
P.S. the team hasn't implemented the consensus algorithm yet. They are publishing their design to collect feedback. So, let the team know what you think on Discord or Telegram (or reply here if you're not on those).