In biology, something like a protein domain is an ideal candidate for a "module" because it is a tool that can be reused at different places to serve different purposes. Nature does not want to reinvent tools; it would be more efficient to reuse existing ones -- protein domains are hard to invent, so it is a perfect item to reuse.
Moving on to network structure. Patters, such as feedback or feed-forward motifs, are not too difficult to reinvent (depending on how hard re-wiring is). For example, re-wiring genetic networks is easy. So it does not make sense to call any genetic network a "module". However, a combination of protein interactions combined with gene regulation might be a module.
For example, lets consider a network composed of a protein that responds to a small molecule and activates a protein that then upregulates a gene. This network is difficult to reinvent because it has multiple interactions that are very specific. It would be a module that is worth reusing. For example, the final gene product can be replaced with some other gene -- a simple way to reuse the module.
As an additional observation, I think it makes sense to say that modules span multiple "layers". For example, in electronics, logic gates convert analog circuits to digital. The example in the previous paragraph is a module that converts small molecule concentrations to gene regulation.