Process of integrating a specific legal contract (which can be built with Legal Markdown or any other contract building system) into a specific smart contract which runs on a distributed data store such as Eris Industries’ Thelonious.
The idea of dual integration is to allow users to be able to have the certainty of having a real world contract which can be taken to a court and enforced using established dispute resolution processes in the jurisdiction(s) of the user(s) while also using a smart contract as the primary mechanism for administering the data-driven interaction which attends to the agreement between the parties.
For another system which is also seeking to bridge this gap see Primavera de Filippi’s Draft Legal Framework For Crypto-Ledger Transactions 
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From Eris website