erhellen
to illuminate
To make something brighter with light or to light it up.
Der Scheinwerfer erhellte die dunkle Bühne.
The spotlight illuminated the dark stage.

to illuminate / clarify
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to illuminate
To make something brighter with light or to light it up.
Der Scheinwerfer erhellte die dunkle Bühne.
The spotlight illuminated the dark stage.

The verb consists of the adjective 'hell' (bright) and the prefix 'er-'. The prefix 'er-' here means 'to make something bright'. As a verb with 'er-', it is inseparable and forms the perfect tense with 'hat'.
Die Kerze hat den kleinen Raum nur schwach erhellt.
The candle only weakly illuminated the small room.
You can tell whether the literal or figurative meaning is intended from the object. If it is a place, e.g. 'Raum' (room), the meaning is literal. If it is an abstract concept, e.g. 'Frage' (question) or 'Hintergrund' (background), the meaning is figurative.
Ein Blitz erhellte kurz den Nachthimmel.
A flash of lightning briefly illuminated the night sky.
In the literal meaning, the subjects are often light sources. Typical formulations are 'die Sonne erhellt den Tag' (the sun illuminates the day) or 'eine Lampe erhellt das Zimmer' (a lamp lights up the room).
Der volle Mond erhellte die nächtliche Landschaft.
The full moon illuminated the nighttime landscape.
In the figurative meaning 'aufklären' (to clarify), 'erhellen' belongs more to elevated written and educated language. It often sounds more elegant or profound.
Die Forschungsergebnisse erhellen die komplexen Zusammenhänge.
The research findings clarify the complex connections.
The reflexive form 'sich erhellen' is used almost exclusively for a person's facial expression. Typical subjects are 'sein Gesicht' (his face), 'ihre Miene' (her expression), or 'sein Blick' (his gaze).
Ihre Miene erhellte sich, als sie das unerwartete Kompliment hörte.
Her expression lit up when she heard the unexpected compliment.
to explain / declare
'erklären' and 'erhellen' can both mean that an unclear matter becomes more understandable. 'erklären' is the normal word when someone makes something understandable to another person. 'erhellen' sounds more elevated and is used more when new information clarifies a problem, a connection, or a difficult question. The words can be confused because both have to do with understanding. In everyday language, 'erklären' is almost always the safer choice; 'erhellen' fits better in texts, reports, or more serious conversations.

Der neue Bericht erhellt, warum das Projekt so teuer geworden ist.
The new report clarifies why the project became so expensive.
In der Küche erklärt sie ihrem Sohn, warum das Wasser kocht.
In the kitchen, she explains to her son why the water is boiling.