One common problem when explaining ideas is that we often jump right into talking about the solution, and just assume prior knowledge of the problem we are talking about.

But since the audience probably doesn't know the problem as intimately as we do, this tends to make our explanation hard to understand - even if our solution is straightforward.

A simple trick I once learned is to structure the explanation into four parts, with one sentence for each part: (1) state the problem, (2) state the consequences of the problem, (3) state the solution, (4) state the consequences of the solution.

Since the explanation now automatically includes both the problem and the solution, it usually is both more compelling and easier to understand.