wahnsinnig
extremely
Colloquially used as an adverb for emphasis: very, extremely, incredibly.
Das Essen in diesem Restaurant ist wahnsinnig lecker.
The food in this restaurant is extremely delicious.

extremely / insane
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extremely
Colloquially used as an adverb for emphasis: very, extremely, incredibly.
Das Essen in diesem Restaurant ist wahnsinnig lecker.
The food in this restaurant is extremely delicious.

The word is made up of 'Wahn' (a false, irrational idea) and 'Sinn' (sense/mind). 'Wahnsinnig' (insane/extremely) originally describes a state in which the mind or senses are clouded.
Der Lärm in der Fabrik war so laut, er machte einen fast wahnsinnig.
The noise in the factory was so loud it almost drove you insane.
In colloquial language, 'wahnsinnig' (extremely) is very often used as an adverb to intensify an adjective or verb. It then simply means 'very' or 'extremely'.
Ich habe mich wahnsinnig über das Geschenk gefreut.
I was extremely happy about the gift.
When 'wahnsinnig' (insane) describes a noun, it means 'crazy' or 'absurd'. Typical combinations are 'eine wahnsinnige Idee' (an insane idea), 'ein wahnsinniger Plan' (an insane plan), or 'ein wahnsinniges Glück' (incredible luck).
Er hatte wahnsinniges Glück, dass er den Zug noch erwischt hat.
He was incredibly lucky to still catch the train.
The original meaning 'psychically ill/mentally ill' is hardly used in everyday language today. You find it mainly in older literature or in a very formal, medical context.
In der Novelle wird die Hauptfigur langsam wahnsinnig.
In the novella, the main character slowly goes insane.
very
'sehr' and 'wahnsinnig' can both make something stronger. 'sehr' is the neutral intensifier and fits in almost all situations. As an intensifier, 'wahnsinnig' means roughly 'very', 'extremely', or 'incredibly', but it sounds more colloquial and more emotional. It works well when you want to express strong joy, stress, cold, or tiredness. In official or factual texts, 'sehr' is better. Also important: in other meanings, 'wahnsinnig' can mean 'crazy' or 'unreasonable'; here, however, the focus is only on its intensifying meaning.

Am Wochenende haben wir uns über den Besuch wahnsinnig gefreut.
At the weekend, we were incredibly happy about the visit.
Nach dem Gespräch mit dem Verkäufer werde ich sehr vorsichtig sein.
After the conversation with the salesperson, I will be very careful.