Bitcoin Forum

We hear plenty of talk of how public blockchains are going to change the world, but to function on a global scale, a shared public ledger needs a functional, efficient and secure consensus algorithm.

A consensus algorithm, like bitcoin's proof of work (the one we hear about most often), does two things: it ensures that the next block in a blockchain is the one and only version of the truth, and it keeps powerful adversaries from derailing the system and successfully forking the chain.

In proof of work, miners compete to add the next block (a set of transactions) in the chain by racing to solve a extremely difficult cryptographic puzzle. The first to solve the puzzle, wins the lottery. As a reward for his or her efforts, the miner receives 12.5 newly minted bitcoins – and a small transaction fee.


Edit:
Full Read Here: http://www.coindesk.com/short-guide-blockchain-consensus-protocols/

The link you provided is wrong. The correct one is:

http://www.coindesk.com/short-guide-blockchain-consensus-protocols/

The guide is informative, but unfortunately has some severe errors. The PoS paragraph only seem to describe the NXT protocol and similar approaches where the stakers only receive the transaction fees, but no variants with continuous minting of fresh coins (like PPC and the extreme cases of Hyperstake etc.), which are very popular in smaller cryptocurrencies.

And for Proof of Burn, the only implementation I know does not let the burners earn a "lifetime privilege" but a privilege that decreases over time and lasts one year as a maximum (At the end, they mention it: "Over time, your stake in the system decays"). And the sentence "the protocol still wastes resources needlessly." is simply false because in PoB no physical resources (only "virtual" ones) are wasted.

So unfortunately the guide has several inaccuracies and stays superficial. That may not be important if you want to get a first impression on "what's possible" but for advanced users it reads pretty odd.