Virtual automated market makers (vAMMs) are covered in full under virtual AMM (vAMM), which explains the mechanism, its history and its weaknesses. This page explains the plural, longer form of the name, which appears in protocol documents and research papers.
An ordinary automated market maker holds two real pools of tokens and sets prices from the ratio between them, so every trade moves tokens in and out of the pool. A virtual AMM keeps the same pricing curve, often the constant-product formula, but the "reserves" are only numbers in a smart contract. Traders post collateral, usually a stablecoin, into a separate vault, and the virtual curve is used to work out the price at which their positions open and close. The formulas behind AMMs therefore still apply, even though no tokens sit in the curve.
The design was built mainly for perpetual futures on a decentralized exchange, where traders want exposure to an asset's price without anyone delivering the asset. Because no liquidity providers are needed, a market can launch quickly. The trade-off is that the virtual curve can drift away from the real market price, so vAMM platforms rely on funding payments and price oracles to pull it back, and several later moved to other models.