In a typical asset swap, a dealer buys a bond from a customer at the
market price and sells to the customer a floating rate note at par. The
dealer then enters into a fixed-for-floating swap with another
counterparty to offset the floating rate obligation and the bond cash
flows.
Similar in structure to a plain vanilla swap, the key difference is the underlying of the swap contract. Rather than regular fixed and floating loan interest rates being swapped, fixed and floating investments are being exchanged.
In a plain vanilla swap, a fixed libor is swapped for a floating libor. In an asset swap, a fixed investment such as a bond with guaranteed coupon payments is being swapped for a floating investment such as an index.