Simply put, a business capability model is a functional breakdown of what a business does, usually going from quite coarse definitions of high-level business functions (think “Product Management”) to a component function at a more detailed level (e.g. “Detailed Design”). How far down do you go? To a level that makes sense for the business (bearing in mind that some functional areas are more critical and/or complex than others, so a deeper dive is warranted) and that describes a useful service that the business provides, either internally or externally. It is not as far down as individual tasks and activities; that is usually too detailed to be useful as a strategic management tool. In practice, it is unusual to get strategic value digging any deeper than 3 − 4 levels; beyond that point it is more likely to be confusing than illuminating.
Why is it useful? A capability model forms a stable base on which to build many analyses of the business, is a touchstone for management conversations by giving a common understanding of the business (the “same page” we’d all like to be reading from), and serves as a foundation for other enterprise architecture tools. How? By being a description of WHAT the business does, which changes slowly and rarely, if at all, over many years. A lot of architecture practices like to start with a process model (which IS a useful tool) that describes HOW the business does things, but not only is that subject to frequent change (even disruption), most businesses are putting significant effort into process improvements; i.e. they are continually trying to change HOW they do things. This makes an unstable basis for strategic business design.
Some other useful definitions and descriptions can be found at these links: