Modularity is the extent to which a system can be divided into clusters. It is a very broad concept which can be applied across many different domains, for example:
In graph theory, modularity can be measured in terms of a graph's structure. For instance, there is a common mathematical definition for graphs, which is based on the idea of modules as partitions of the nodes of a graph, with more edges within modules than would be expected by chance.
In evolutionary biology, modularity has been observed at many different levels, from protein structure to organ systems. There is currently no universally accepted explanation for why modularity seems to have been produced by evolution, and less so by genetic algorithms, although there are widely-held theories (most notably the idea of modularly varying goals, as proposed by Kashtan & Alon).
Modularity may be highly relevant for alignment research, because the more modular a system is, the greater the chances that we will be able to understand the cognition it is performing in terms of high-level abstractions.