
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.

to clarify
To make an unclear or complex matter understandable or to shed light on it.
Die neuen Dokumente halfen, die Hintergründe der Affäre zu erhellen.
The new documents helped clarify the background to the affair.

to light up
Refers to a face or expression that suddenly brightens and appears friendlier because of joy or realization.
Als sie die gute Nachricht hörte, erhellte sich ihr Gesicht.
When she heard the good news, her face lit up.
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 illuminate / examine
Beleuchten and erhellen can both refer to making something brighter and visible. Beleuchten focuses more on the target that the light falls on; erhellen emphasizes increasing brightness. Use beleuchten for an object being lit directly and erhellen for a room becoming brighter.

Das Morgenlicht erhellt den ganzen Zuschauerraum.
The morning light brightens the entire auditorium.
Ein Scheinwerfer beleuchtet die Bühne.
A spotlight illuminates the stage.