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I heard Luca Cardelli, who's also worked on programming languages and typing systems, give this talk. He gives an overview of the programming language technology to program biological matters. This field has been brewing for a decade or so, but it's now seemingly acquired critical mass.

Deeply fascinating.

This is extremely interesting!

Can someone articulate the relationship between this concept (molecular programming) and 'nanotechnology'?

Nanotechnology is more general as it pertains to all manipulation of matter on an atomic, molecular, and supramolecular scale. Cardelli's work is primarily geared towards DNA-based mechanisms.

Could be like making a programming language for legos. It's interesting but does the abstraction make sense?

For legos, language does a bad job of describing geometric structures. A 3D modeling tool serves as a better interface in this case.

For molecules it's weirder. I'm not sure how it would work in terms of proteins or dna.

The research hypothesis is that the programming languages Cardelli develops do a reasonable job, and there are examples where they have delivered better predictions than differential equation based approaches.

Molecular Programming – The systematic manipulation of matter (2014) [pdf]