I write this from my phone, so I can't find the links to docs in an easy manner. I'll try to explain this as easy as possible: blockchains are distributed ledgers that can store information that can't be altered. They're mostly used now to store transactions info, but they can store anything. In a distributed app the blockchain would be the db. In order to store info on the blockchain one has to pay a transaction fee to the network. This transaction fee goes to the miners that validate the transaction. The ethereum network (and some others) can execute smart contracts: each node is able to execute such a contract. On the ethereum network, smart contracts are written in a language called solidity, which is similar to js. Having a smart contract executed also require a small amount to be paid. Smart contracts can interact with the blockchain: store and retrieve info from it, so the smart contract would be your PHP equivalent. The front end part is done on ethereum using their own, open source client, called mist. Mist is basically an electron app which can interact with an ethereum node. In order to use a distributed app, one has to use a smart contract, which resides at an address in the blockchain, using mist.

Of course, having all the dbs of all the apps replicated in every node is not really optimal and that will be solved using sidechains.