I've learned that both ekspliki and klarigi mean to explain. Is there a difference in meaning? In nuance? In use?
The standard word for "explain", klarigi, means "to make clear, to clarify" and this has literal significance as well as figurative. In addition, it strongly implies that the explanation was successful. So does komprenigi ion al iu.
Ekspliki has a fussy, formal sound. I'd be tempted to call a baffling explanation an ekspliko rather than a klarigo.
The root eksplik- does not exist in Akademia vortaro. So I recommend to prefer klarigi over ekspliki as it is more Esperantesque. There's no clear difference in the meaning. I never use ekspliki and, according to my experience, klarigi is way more common. eksplik- is probably a francism.
Esperanto word derivation rules have been crafted, and Esperanto roots chosen, so that very often a word formed according to the internal rules of Esperanto is also immediately recognisable as Esperanto's version of an international word. But sometimes this fails. This can result in Esperanto words such as malsanulejo that can be puzzling to beginners, and also to words such as klarigi that are used in ways that are not completely predictable from the international vocabulary. (Klarigi doesn't just mean clarify; it also means explain.) In such cases, it is not surprising and in fact not necessarily a bad thing that the corresponding international words (such as hospitalo or ekspliki) also enter the language.
Most natural languages have a similar tension between international vocabulary and whatever the original language stock and its word building rules are.
- Sometimes one is much stronger than the other. For example in English, the international (Graeco-Roman) vocabulary has practically replaced Germanic words completely. You wouldn't normally refer to a hospital as a "sick house", and teachers will normally "explain" things, not "spell them out".
- Other languages, such as German or Turkish, have at some point undergone a process in which foreign/international terms (mostly French and Latin in the case of German; mostly Persian and Arabic in the case of Turkish) were replaced by new words that follow the internal logic of the language. In such a case, the earlier foreign word may disappear or both words may exist in parallel, basically as synonyms though usually with at least slight differences in meaning.
- The Romance languages are special in that their root vocabulary and internal logic basically agrees with those of the most important international words.
Therefore, Esperanto speakers are not the first who have to deal with the problem. I think a good approach was used by German writers at a time when the German literary standard was still relatively new and one could not expect readers from every region to understand it easily. I am under the impression that they often used the rhetorical figure known as synonymia. If you want to write exceptionally clearly addressing a wide variety of readers from all over the world, you may want to write like this:
- La instruisto klarigis kaj explikis ĉion.
- Li iris al hospitalo kaj malsanulejo.
But if you can assume that your readers have full command of the language, you can just pick one of the synonyms. If you are purist, you may want to prefer the word that follows Esperanto's internal logic, no matter what. But you can also use the situation to express fine nuances. E.g., klarigi doesn't just mean explain. It quite obviously also means clarify. This makes it possible to carry over the explain/clarify distinction from English or other languages to Esperanto. (I think it works roughly like this: Explaining is primarily concerned with the process of talking about something in the hope that this will clarify it. Clarifying is about the success of the explanation. "The teacher explained and explained, but didn't actually manage to clarify anything.")