Dapp is short for Decentralized Application. This refers to an application that runs on a decentralized collection of computers and servers, either through a peer-to-peer network such as Tor, or on a blockchain such as Ethereum. This keeps the application from the control of a centralized authority.
In standard web applications the backend software runs on a network that is owned and operated by a single organization, such as Twitter or YouTube (owned by Alphabet). This means the owner has control over what is allowed on the application, and can block or remove items at their discretion.
With a Dapp, such as one run on a blockchain, the application is running on a decentralized network and is free from the control of any single entity. Once content is added it is part of the blockchain and will exist there for as long as the blockchain exists. One very good current example of this is the Steem blockchain, which currently has a Reddit-like Dapp, a Twitter-like Dapp, and a YouTube-like app, all running on the same blockchain.