E.g. let's say you make a trading card game. The art assets, GUI, etc. are all stored in a conventional webpage. However, the 'owner' of each card is stored in the blockchain by associating the unique digital identifier for each card with some key. You go on the website and want to trade your card for another (owned by someone else). Both you and other person interact with the web page, which in turn translates these interactions into function calls to the functions written in the smart contract, which ultimately comprises a blockchain transaction, and you sign the transaction using your private key (proving you own the digital asset in question). The VM would execute these transactions in accordance with the code of the DApp, and when the transactions are processed the new block would state that each card now belongs to the new owner.