There's a lot of humanity problems solving talk in cryptocurrency land. I think it's because the people that run in that scene can finally glimpse what this technology can do, when wielded correctly. That said, there's still a lot to do before we replace the government with a crypto contract!
Ethereum uses a cryptocurrency under-the-hood called 'ether', which pays for 'gas': compute resources like networking, storage and compute. These resources are used in a decentralized way by programs which are capable of carrying their own cryptocurrency wallets. As long as the programs can pay for their own existence, they get to keep running on the network. Like Bitcoin, the network is comprised of a bunch of 'miners' that provide the resources for running the code. You could run a miner if you wanted to. Unlike Bitcoin, the code keeps running as long as it can pay for the resources it uses. I could write some code that does this, if I wanted to.
In theory, you could create some code, have it generate a wallet, pay the wallet, and then let the little guy go wander off onto the network doing things. BTW, this little guy I'm describing is called a DAC, for decentralized autonomous corporation (or smart contracts). The 'things' it can do are limited, but it can, in theory, pay for stuff or pay other DACs, access storage, do computations, and access the network. Keep in mind this is isn't a NodeJS application framework you are dealing with here. Ethereum is primarily designed for implementing logically governed contracts between entities that need to exchange value. It's like Bitcoin scrypt on steroids, without the possibility of a halting-state. In theory.
Fun fact: Bitcoin scrypt doesn't support loops, so it's limited in scope in what it can do with a given transaction. Not so with Ethereum.