First, thank you for a terrific question! To answer it, let's first clarify what is the object of explanation -- what is it that we are trying to explain? I would propose that the answer is this: We explain our ideas.
Now, ideas come in two distinct flavours. John Locke referred to the two as the simple and the complex ideas respectively. The simple ideas are statistical models encompassing a person's lifetime of experiences and, as such, they are unexplainable. An example of a simple idea is philosophers' favorite, "What is a chair?" Or what is a woman, etc.
The statistical processing behind simple ideas occurs entirely in our subconsciousness. Only the bottom line of that processing is communicated to our conscious awareness as a feeling -- as intuition. We don't know how do we know that we are looking at a chair, we just do! Or, to be more precise, we feel confident that that things is, in fact, a chair. So confident, this intuition feels like knowledge (and, therefore, explainable), even though it still is just a guess. And, of course, not every intuition is this certain.
Our complex ideas is a very different animal. I am going to refer to them simply as models because they are not merely imitating knowledge -- they are it, the knowledge. Collectively, they represent a virtual reality that we visualize in order to understand how the real thing -- the real world -- works. Each such model is a virtual machine -- it has moving parts, and it performs work producing virtual outcomes that match the outcomes we see in real life. And the model's purpose is to simulate a real-life process that produces those outcomes -- for example, it could be a model of the solar system, or of the banking system, or of a mental condition. Or a model of the human mind.
This, then, is what we are trying to describe whenever we explain things -- the models that we visualize. And the purpose of the explanation is for the listener to reconstruct the same models in their minds. It is not an easy task, trying to describe a vision with words. That's why visual aids, such as diagrams or animations, can be of great help. Untimely, the communication is successful when the listener sees in their minds what the speaker sees in theirs; and when the listener succeeds at fitting that new model into their larger simulation -- their understanding -- of the Reality.