If you elucidate something, you explain it very clearly. If you don't understand fractions, a visit to the pie shop may elucidate the subject for you.
Elucidate, meaning "to make clear," is from the Late Latin elucidare, from the Latin prefix e-, "thoroughly," and lucidus, "clear, bright." See the word lucid in elucidate? That's an adjective which describes someone who thinks clearly or something that is clear enough to understand.