brennend
burning
Being in the state of combustion; standing in flames.
Die Feuerwehr konnte das brennende Auto schnell löschen.
The fire department was able to quickly put out the burning car.

burning
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burning
Being in the state of combustion; standing in flames.
Die Feuerwehr konnte das brennende Auto schnell löschen.
The fire department was able to quickly put out the burning car.

'Brennend' (burning) is the present participle of the verb 'brennen' (to burn). All meanings, including the figurative ones, derive from the idea of burning, heat, or intensity.
Eine brennende Kerze stand auf dem Tisch.
A burning candle stood on the table.
You can recognize the literal meaning 'in Flammen stehend' (standing in flames) by the fact that the adjective describes a noun that can physically burn, such as a house, wood, or paper.
Die Kinder saßen um das brennende Lagerfeuer.
The children sat around the burning campfire.
In the meaning of 'dringend' (urgent) or 'wichtig' (important), 'brennend' (burning) often appears with abstract nouns such as 'Frage' (question), 'Thema' (topic), 'Problem' (problem), or 'Interesse' (interest).
Das ist zurzeit ein brennendes Thema in der Politik.
That is currently a burning issue in politics.
'Brennend' (burning) is especially often used as an adverb with the verb 'interessieren' (to interest). The expression 'Das interessiert mich brennend' means 'That interests me very much'.
Mich würde brennend interessieren, was er dazu gesagt hat.
I would be very interested to know what he said about it.
To express strong, passionate feelings, 'brennend' (burning) is combined with nouns such as 'Wunsch' (desire), 'Sehnsucht' (longing), or 'Liebe' (love).
Er verspürte eine brennende Sehnsucht nach seiner Heimat.
He felt a burning longing for his homeland.
important
'wichtig' and 'brennend' can both express that something has great significance. 'wichtig' is neutral and fits in almost all situations. 'brennend' is stronger and more figurative. It fits especially when a question, problem, or topic is very urgent or strongly occupies many people. So you would more likely say 'eine wichtige Information' (an important piece of information), but 'eine brennende Frage' (a burning question) when you urgently need an answer.

Nach dem Gespräch hatte Anna noch eine brennende Frage.
After the conversation, Anna still had a burning question.
Bei schlechtem Wetter ist es wichtig, genug Zeit für den Weg einzuplanen.
In bad weather, it is important to allow enough time for the journey.