A module is a component which can be replaced by any valid alternative in a specified framework or system.
Modular is a trait of systems which use modules as primary components.
Modularity is a type of composability. A composable system is clearly modular if multiple alternatives are available for some or all of the systemic nodes.
In strict formal design contexts, modules must be specified, and their specifications must indicate required traits. Clear definitions facilitate the independent development of valid alternative modules. However, to create highly useful modularity, specifications must be relatively generic.
Crucially, the (explicitly or implicitly indicated) interfaces of modules enable agents to remove or replace them with other components which possess the required traits.
Some agents use the term modular especially for physical tools and, by extension, the design of systems of modular physical tools. However, modular design is common in software development. Also, agents often use at least somewhat modular creative techniques to pursue complex goals in many specialized activities, even when the products of such activities are not offered to potential users in modular forms.