The books Agile Software Development, Principles, Patterns, and Practices and Agile Principles, Patterns, and Practices in C# are the best resources for fully understanding the original goals and motivations behind the Dependency Inversion Principle. The article "The Dependency Inversion Principle" is also a good resource, but due to the fact that it is a condensed version of a draft which eventually made its way into the previously mentioned books, it leaves out some important discussion on the concept of a package and interface ownership which are key to distinguishing this principle from the more general advise to "program to an interface, not an implementation" found within the book Design Patterns (Gamma, et. al).
To provide a summary, the Dependency Inversion Principle is primarily about reversing the conventional direction of dependencies from "higher level" components to "lower level" components such that "lower level" components are dependent upon the interfaces owned by the "higher level" components. (Note: "higher level" component here refers to the component requiring external dependencies/services, not necessarily its conceptual position within a layered architecture.) In doing so, coupling isn't reduced so much as it is shifted from components that are theoretically less valuable to components which are theoretically more valuable.
This is achieved by designing components whose external dependencies are expressed in terms of an interface for which an implementation must be provided by the consumer of the component. In other words, the defined interfaces express what is needed by the component, not how you use the component (e.g. "INeedSomething", not "IDoSomething").
What the Dependency Inversion Principle does not refer to is the simple practice of abstracting dependencies through the use of interfaces (e.g. MyService → [ILogger ⇐ Logger]). While this decouples a component from the specific implementation detail of the dependency, it does not invert the relationship between the consumer and dependency (e.g. [MyService → IMyServiceLogger] ⇐ Logger.
The importance of the Dependency Inversion Principle can be distilled down to a singular goal of being able to reuse software components which rely upon external dependencies for a portion of their functionality (logging, validation, etc.)
Within this general goal of reuse, we can delineate two sub-types of reuse:
Using a software component within multiple applications with sub-dependency implementations (e.g. You've developed a DI container and want to provide logging, but don't want to couple your container to a specific logger such that everyone that uses your container has to also use your chosen logging library).
Using software components within an evolving context (e.g. You've developed business-logic components which remain the same across multiple versions of an application where the implementation details are evolving).
With the first case of reusing components across multiple applications, such as with an infrastructure library, the goal is to provide a core infrastructure need to your consumers without coupling your consumers to sub-dependencies of your own library since taking dependencies upon such dependencies requires your consumers to require the same dependencies as well. This can be problematic when consumers of your library choose to use a different library for the same infrastructure needs (e.g. NLog vs. log4net), or if they choose to use a later version of the required library which isn't backward compatible with the version required by your library.
With the second case of reusing business-logic components (i.e. "higher-level components"), the goal is to isolate the core domain implementation of your application from the changing needs of your implementation details (i.e. changing/upgrading persistence libraries, messaging libraries, encryption strategies, etc.). Ideally, changing the implementation details of an application shouldn't break the components encapsulating the application's business logic.
Note: Some may object to describing this second case as actual reuse, reasoning that components such as business-logic components used within a single evolving application represents only a single use. The idea here, however, is that each change to the application's implementation details renders a new context and therefore a different use case, though the ultimate goals could be distinguished as isolation vs. portability.
While following the Dependency Inversion Principle in this second case can offer some benefit, it should be noted that its value as applied to modern languages such as Java and C# is much reduced, perhaps to the point of being irrelevant. As discussed earlier, the DIP involves separating implementation details into separate packages completely. In the case of an evolving application, however, simply utilizing interfaces defined in terms of the business domain will guard against needing to modify higher-level components due to changing needs of implementation detail components, even if the implementation details ultimately reside within the same package. This portion of the principle reflects aspects that were pertinent to the language in view when the principle was codified (i.e. C++) which aren't relevant to newer languages. That said, the importance of the Dependency Inversion Principle primarily lies with the development of reusable software components/libraries.
A longer discussion of this principle as it relates to the simple use of interfaces, Dependency Injection, and the Separated Interface pattern can be found here. Additionally, a discussion of how the principle relates to dynamically-typed languages such as JavaScript can be found here.
