
schnallen
to get
Colloquial for to understand or grasp.
Ich habe es ihm dreimal erklärt, aber er hat es einfach nicht geschnallt.
I explained it to him three times, but he just didn't get it.
to get / to buckle
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to get
Colloquial for to understand or grasp.
Ich habe es ihm dreimal erklärt, aber er hat es einfach nicht geschnallt.
I explained it to him three times, but he just didn't get it.

to buckle
To fasten or close something with a buckle, that is, a clasp made of metal or plastic.
Sie schnallte den Riemen ihrer Sandale fest.
She buckled the strap of her sandal tightly.

to tighten one's belt
An idiom meaning that you have to save money and get by with less.
Nach dem Jobverlust musste die Familie den Gürtel deutlich enger schnallen.
After the job loss, the family had to tighten their belts considerably.
The verb 'schnallen' (to buckle) is derived from the noun 'die Schnalle' (the buckle/clasp). This explains the literal meaning of fastening something with a buckle.
Der alte Koffer hatte noch Riemen, die man schnallen musste.
The old suitcase still had straps that had to be buckled.
You can recognize the colloquial meaning 'verstehen' (to understand) by the fact that the object is often abstract, e.g. 'es' (it), 'das' (that). The literal meaning 'befestigen' (to fasten) is used with concrete objects like 'Gurt' (belt/strap) or 'Riemen' (strap).
Nach deiner Erklärung habe ich es endlich geschnallt!
After your explanation, I finally got it!
The meaning 'verstehen' (to understand) or 'begreifen' (to grasp) is very colloquial. In formal or written contexts, you should avoid this word.
Komm, beeil dich, schnallst du es nicht? Wir müssen los!
Come on, hurry up, don't you get it? We have to go!
In its literal meaning, 'schnallen' (to buckle) is often used with objects that have a clasp or buckle. Typical phrases are 'den Gürtel schnallen' (to buckle the belt), 'den Helm schnallen' (to fasten the helmet), or 'die Riemen schnallen' (to buckle the straps).
Vor dem Start der Achterbahn muss man den Sicherheitsbügel festschnallen.
Before the roller coaster starts, you have to fasten the safety bar.
The idiom 'den Gürtel enger schnallen' (to tighten one's belt) is a fixed unit. It means that one has to save money, and the person who has to save is the subject of the sentence.
Wegen der hohen Inflation müssen viele Leute den Gürtel enger schnallen.
Because of high inflation, many people have to tighten their belts.
to understand / grasp
Begreifen and schnallen can both mean understanding a difficult explanation. Begreifen is the neutral standard-language choice, while schnallen is clearly more colloquial and often sounds more casual. Begreifen is more suitable in a formal context; schnallen is possible in a relaxed conversation.

Nach der Erklärung konnte ich endlich schnallen, warum der Termin verschoben wurde.
After the explanation, I could finally get why the appointment had been postponed.
Nach der Erklärung konnte ich endlich begreifen, warum der Termin verschoben wurde.
After the explanation, I could finally understand why the appointment had been postponed.