Modularity is a concept used in many disciplines that deal with complex systems. There are two related ideas under the concept of modularity.
In a top-down approach, a complex system should be decomposed in a way that makes the parts independent from each other in order to prevent the propagation of change and error. This is related to the idea of black-box abstraction.
In a bottom-up approach, we want to be able to easily rearrange the parts of the system to change its behavior. The metalinguistic abstraction is one technique to create modular systems in this sense.
Those two ideas are related because they depend on the type of coupling between the parts of the system.
Propagation of Change
One reason to create modular systems to prevent the propagation of change. If a change in a part of a system generates one or more changes in other parts, we make the system harder to maintain. We want to be able to evolve the parts of our system independently.
In Notes on the Synthesis of Form, Christopher Alexander explains why such decoupling is desirable and how to model design problems to maximize this decoupling.
The first axiom of the Axiomatic Design method is to keep functional requirements uncoupled in the design. We want to be able to adjust the design parameter of a requirement without affecting other requirements.
David Parnas's concept of "information hiding" is similar. Parnas recommends isolating the design decisions into different software modules so we can independently change them as the requirements change.
Propagation of Errors
In software engineering, we also create modules to contain faults and prevent failures to propagate.
We can deploy our systems in different geographical regions, on different servers, in different processes...
What Modularity Is Not
Not all decompositions of a system are modular. One could break down a system into small parts that are not independent from each other and that cannot be rearranged easily.
A module is sometimes defined as a collection of parts that are strongly connected among themselves (high cohesion) but weakly connected to the parts in other modules (loose coupling). However, it makes the definition of modularity non-recursive. It is not clear to me why you would not want the same property inside and outside the module.