EDIT: The wikipedia article is easy to find[1]. However it is really short, looks incomplete, and has a lot of “citation needed” after each point. So I would rather ask on HN.
Proof-of-work works (very broadly) by computers solving harder and harder math problems to create value. Eventually, these get so hard that solving one requires either joining a pool or a huge investment in electricity and mining rigs - which is where we're at now. This isn't good for the environment.
Proof-of-stake works by individuals "staking" some of their own coins to be more likely to be randomly chosen to "validate" a transaction (which earns them a reward, similar to hashing). Validating a transaction is trivial and uses very little electricity, but the rest of the network also checking the transaction keeps the validator honest.
While proof-of-work and proof-of-stake are both a kind of "the rich get richer" game, to get more coins in proof-of-stake all that's required is a greater investment into the network, as opposed to the mining rigs and large amounts of electricity that are required by proof-of-work.
I found this video to be helpful in visualizing the networking parts of proof-of-stake.
Staking better aligns incentives when compared to mining and most other alternatives.
Blockchains that allow protocol changes via votes are an option, and how you quantify votes is a parameter, but PoS is not tied to being a government token, and 'votes' on forks (its really not a vote as both protocols exist after a fork) are made by large and small holders alike. It has nothing to do with amount of currency owned.
Compared to PoS where the biggest incentive is to be nice.
If a validator approves a fraudulent transaction (as determined by other validators), they lose their stake.
Here is one link, and you can find several more.
https://download.wpsoftware.net/bitcoin/pos.pdf
Now, that is a PDF, and I do not recommend blindly opening PDFs. This is by Andrew Poelstra, who is a mathematician at Blockstream.
But how does in know which copy is the real one and not one cooked up by someone like me showing I own half the coins?
With proof of work you can choose the one with the most work in it and that's hard to fake as the real bitcoin blockchain has billions of dollars worth of computer work in.
With proof of stake it's hard. If there is no real cost, fakers can make thousands or millions of fake chains and how do you know which is the 'real' one?
There are potential solutions but it's tricky. Like if you have www.stake-coin.com point to the real one, what if someone manages to take over the domain?
Im kinda at a loss about what other vectors of attack possible, hard to find any digestible info, and pos protocol designs are really complex.