A cross-chain bridge is another name for a blockchain bridge, a protocol that lets tokens or messages pass between blockchains that cannot otherwise communicate. The words cross-chain simply stress that the transfer crosses from one network to another, for example from Ethereum to Solana or to a layer-2 network.
Most bridges do not physically move an asset. The user deposits tokens into a contract or custodian on the source chain, where they are locked, and an equivalent amount of wrapped tokens is issued on the destination chain; sending the wrapped tokens back releases the originals. Other designs use pools of liquidity on each side, or burn the token on one chain and mint it natively on the other. The latter is how some stablecoin issuers move their own coins, as with Circle's Cross-Chain Transfer Protocol for USDC.
Bridges matter for payments because stablecoins are issued on many networks, and a payer and recipient may hold them on different ones. They are also a concentrated point of risk. Faults in bridge contracts and stolen validator keys have caused some of the largest thefts in cryptocurrency, and bridges are used to obscure fund flows, which is why blockchain analytics firms trace transfers across them.