Ethereum is a blockchain technology that, among others, allows to create programs on the blockchain, called smart contracts. The main Ethereum network is the second most important capitalization in the cryptocurrencies industry with 13 billion dollars, after Bitcoin. Ethereum's cryptocurrency is called Ether. It's easy to create cryptocurrencies with smart contracts by derivating generally accepted models like ERC 20: the tokens. Ethereum can also be used to build private blockchains.
Ethereum smart contracts are bytecode deployed by normal transactions. Therefore, they can not be deleted or modified. So their users are guaranteed that the code can never be modified even by their author.
In blockchain, a wallet is a tool to manage a blockchain account. Often, those wallets allow to access the blockchain through external services, in order to avoid having to install the whole blockchain. On Ethereum, the most known wallet is Metamask.
A decentralized application, or dApp, generally involves smart contracts as well as a user interface which is generally hosted on classic computing. dApps ask the permission to use the user's wallet but never access the private keys.