What does this do? Let's break down the description from the site:
> Cello converts electronic design specifications of combinational logic to complete DNA sequences encoding transcriptional logic circuits that can be executed in bacterial cells. A database of transcriptional repressors characterized in the Voigt lab provide genetic NOT gates and NOR gates that can be composed into any logic function.
Transcription is the process by which a cell copies DNA into RNA. The RNA then can be used for many processes, of particular importance as a template for proteins. (This is called the central dogma of biology. DNA->RNA->Protein.)
Transcription is evoked by proteins that bind to the DNA. One protein might bind to a particular motif (a DNA sequence) and recruit (bind with) other proteins that then drive the translation of the DNA sequence into RNA. (Where does the energy for this process come from? From nucleoside triphosphates from which the growing RNA sequence is built.) Meanwhile, another protein may bind to the DNA and block the passage of the translation machinery, thus turning off expression of the gene.
These interactions can be thought of as encoding a logical system. What Cello does is provide a programming language to describe them which can be compiled into the DNA sequences that completely encode the proteins and motifs for the entire system.
> Does the machinery in the cell just randomly bind to plasmids and do what they say?
Basically, yes. At the scales we are thinking about concepts from quantum mechanics may be more apt. If we imagine the proteins classically, we can think of them as spinning at a million cycles a second and rapidly traversing the volume of the cell. In effect, everything in the cell is interacting with everything else at relatively short time scales.