Formal:
* Articulated: Suggests a clear and precise explanation.
* Elucidated: Implies making something previously unclear, understandable.
* Expounded: Indicates a detailed and comprehensive explanation.
* Illustrated: Means to clarify with examples or visuals.
* Demonstrated: Suggests a practical explanation, often with a visual element.
Informal:
* Broke down: Suggests simplifying a complex idea.
* Clarified: Indicates removing any confusion.
* Put into words: Implies expressing something verbally.
* Made sense of: Indicates bringing understanding to a confusing situation.
* Spelled out: Implies making something very clear and explicit.
Other options:
* Discussed: Suggests an open conversation or debate.
* Described: Focuses on the details of something.
* Revealed: Implies the uncovering of something previously hidden.
* Showed: Implies a visual demonstration or explanation.
* Convinced: Indicates successfully persuading someone to understand.
The best word to use depends on the specific context and the desired tone.