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In traditional finance, an IOU is a document that acknowledges a debt owed. In business, accounts receivable may be informally called IOUs.
In modern finance, blockchain and cryptocurrency, an IOU is essentially a token, issued on the blockchain, representing the same value as the underlying asset. For example, 1 BLOCKBASIS.BTC is equal to 1 BTC. The BLOCKBASIS.BTC tokens run on Bitshares and hence the Graphene blockchain, while the 1 BTC is powered by the Bitcoin blockchain.
By introducing an IOU, platforms like Blockbasis is able to transfer and trade different cryptocurrencies with different blockchains, on the same blockchain. This brings downs cost and time tremendously when one user needs to transfer or trade cryptocurrency with another user.