In the context of peer-to-peer systems, "smart assets" are unique virtual tokens of ownership that can be controlled or exchanged using smart contracts.
The smart asset may be a virtual representation of a physical asset, such as a house or a car; a smart asset could also represent non-physical goods such as a bitcoin, a share in a corporation, or access rights to a song.
What may be done with a smart asset is defined by the smart contract that is attached to it. Some smart contracts can be very simple: transfer of ownership of the smart asset requires a signature from the private key of the current owner. These contracts can also be much more complex, involving keeping money in escrow, interfacing with 3rd party systems, involving multiple users, etc.
Smart assets and their associated smart contracts are recorded on a peer-to-peer system (ex: Bitcoin, NXT, Ethereum, or one of many other blockchains or peer-to-peer system). Smart assets are seen as having a certain degree of autonomy because their existence is guaranteed and secured by a peer-to-peer network. An important feature of P2P networks is that they do not have a single point of failure or control; this ensures that a smart asset cannot be manipulated or exchanged without meeting the specific conditions of the smart contract.
Smart assets are an important innovation because they are unique and scarce. Prior to their invention, digital goods were easily copied and transfered; this cannot be done with a smart asset without satisfying the smart contract conditions.