Each ten centimeter cube is an autonomous unit with a microprocessor and a set of instructions on how to link themselves with other modules.

For example, four blocks piled up on top of each other to form a tower can create another identical tower by swiveling around and picking up other blocks and piling them up. Obviously, much larger and more complex structures can be built by expanding on this model.

(From Self-Replicating Machine Pictures)

The self-reproducing machines demonstrate here are essentially modular robots, composed of multiple identical actuated modules with electromagnets to selectively weaken and strengthen connections so as to determine where the structure breaks and joins. Each module is a 10cm cube, split into two halves... One half of the cube can swivel relative to another half in increments of 120°, each time cycling three faces of the cube. Connected cubes can thus form and reconfigure into arbitrary morphologies... The cubes are powered at the base and transfer data and power through their faces. The control of the machine is distributed among the modules: A microcontroller onboard each module executes a motion schedule governed by time and contact events.
(From Self-reproducing Machines pdf)

John von Neumann was the first scientist to do rigorous work on the topic of self-replicating machines. However, science fiction author Philip K. Dick beat him to the punch with his 1955 short story Autofac, which described an automated factory that also had the capacity to reproduce itself by shooting tiny pellets full of nanomachines into the distance:

"They're building," O'Neill said, awed. He got up and prowled on. Off to the side, at the far edge of the gully, he came across a downed pellet far advanced on its construction...

This one had made great enough progress to be identified. Minute as it was, the structure was familiar. The machinery was building a miniature replica of the demolished factory.
(Read more about Philip K. Dick's autofac)

I'd also add a reference to a more structured version of this idea, the Robot Cells (Crystal-Shaped Modules) from 1987 work by Michael P. Kube-McDowell.

The concepts explored by these simple modules may also have applications on other planets:

Self-replication could have major implications for how robots are used in remote environments where repairing them is difficult. "Self-replication is the ultimate form of repair," Lipson says. "You can imagine robotic systems on Mars or at the ocean bottom repairing themselves using a mechanism like this."