Here's a quick summary.
The overall configuration is fundamentally identical to a basic refrigerator.
The difference is that instead of using a compressor to cause phase change in a fluid, they pass water over blocks of material that are either hot or cold.
The materials are made hot or cold by the application of a field, which changes the alignment of the magnetic moments.
When they apply the field, it necessarily adds energy (heat) to the block and when they remove the field, the magnetic moments redistribute and it releases the heat.
The rest is just a series of bog standard pumps and radiators.