
unverständlich
unintelligible
Formulated or made in such a way that one cannot understand or make sense of it; unclear or meaningless.
Er murmelte etwas Unverständliches in seinen Bart.
He muttered something unintelligible into his beard.
incomprehensible
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unintelligible
Formulated or made in such a way that one cannot understand or make sense of it; unclear or meaningless.
Er murmelte etwas Unverständliches in seinen Bart.
He muttered something unintelligible into his beard.

incomprehensible
In relation to an action or behavior: not understandable or logically explainable.
Es ist mir unverständlich, warum sie das Angebot abgelehnt hat.
It is incomprehensible to me why she turned down the offer.
The word is logically built: the prefix 'un-' means 'not'. The word 'verständlich' (understandable) comes from the verb 'verstehen' (to understand). So 'unverständlich' literally means 'not understandable'.
Seine Handschrift ist so klein, sie ist fast unverständlich.
His handwriting is so small that it is almost unintelligible.
If 'unverständlich' refers to speech, writing, or sounds, it means that you cannot decode something acoustically or in terms of content. If it refers to actions or decisions, it means that you cannot understand the logic or motivation behind them.
Der Arzt sprach so schnell, dass seine Erklärung unverständlich war.
The doctor spoke so quickly that his explanation was unintelligible.
To express that you personally cannot understand something, the fixed structure 'Es ist mir unverständlich, warum/dass ...' (It is incomprehensible to me why/that ...) is often used. The person who does not understand something is in the dative.
Es ist mir unverständlich, warum er so wütend geworden ist.
It is incomprehensible to me why he got so angry.
unclear
“Unklar” and “unverständlich” can both describe an explanation that is difficult to understand. An “unklare” explanation leaves important points open or allows multiple interpretations, but it may still be partly understandable. An “unverständliche” explanation cannot be understood at all. The key difference is the extent of understanding.

Die Erklärung ist wegen der vielen fehlenden Schritte völlig unverständlich.
The explanation is completely incomprehensible because many steps are missing.
Die Erklärung ist an einer Stelle unklar, weil zwei verschiedene Termine gemeint sein könnten.
The explanation is unclear in one place because it could refer to two different dates.