
begreifen
to understand / grasp
To grasp and understand a complex or abstract matter with the mind.
Ich kann einfach nicht begreifen, warum er so gehandelt hat.
I simply can't understand why he acted that way.
to understand / grasp
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to understand / grasp
To grasp and understand a complex or abstract matter with the mind.
Ich kann einfach nicht begreifen, warum er so gehandelt hat.
I simply can't understand why he acted that way.

to grasp / feel
To touch and feel something with the hands in order to perceive it. This meaning is rarer and often elevated or literary.
Blind versuchte er, die Form der Statue mit den Händen zu begreifen.
Blind, he tried to grasp the shape of the statue with his hands.
'Begreifen' (to understand/grasp) is an inseparable verb made up of the prefix 'be-' and the verb 'greifen' (to grasp). It transfers the idea of physically grasping something to mentally grasping a concept.
Er hat die Regeln des Spiels schnell begriffen.
He quickly grasped the rules of the game.
'Begreifen' (to understand/grasp) is very often used with a subordinate clause that begins with 'dass' (that), 'warum' (why), or 'wie' (how). This expresses which matter is or is not understood.
Ich begreife nicht, wie das passieren konnte.
I don't understand how that could happen.
'Begreifen' (to understand/grasp) often expresses a deeper, more comprehensive understanding that goes beyond simply taking in information. It often implies that you grasp the full implications or the emotional aspects of something.
Erst nach dem Gespräch begriff sie die Konsequenzen ihrer Entscheidung.
Only after the conversation did she grasp the consequences of her decision.
The literal meaning 'etwas mit den Händen greifen' (to grasp something with the hands) is very rare today. It is used almost only in literary or very elevated texts.
Mit seinen Händen versuchte er, die kalte Oberfläche des Steins zu begreifen.
With his hands, he tried to grasp the cold surface of the stone.
to understand
Verstehen and begreifen both refer to grasping something mentally. Begreifen often emphasizes a deeper understanding of a difficult or abstract matter, which sometimes only develops after prolonged thought. Verstehen is the more general choice when the meaning is clear.

Nach langem Nachdenken begreife ich endlich die schwierige Regel.
After thinking about it for a long time, I finally grasp the difficult rule.
Nach der Erklärung verstehe ich die schwierige Regel.
After the explanation, I understand the difficult rule.