groschen
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the penny dropped
An idiom meaning that someone finally understood something after thinking about it for a while.
Nachdem sie es mir zum dritten Mal erklärt hatte, ist bei mir endlich der Groschen gefallen.
After she had explained it to me for the third time, the penny finally dropped for me.
The idiom 'der Groschen ist gefallen' (the penny has dropped) means that someone finally understands something. The person who understands it is often expressed with 'bei' + dative (bei mir, bei dir, bei ihm).
Als ich die Grafik sah, ist bei mir endlich der Groschen gefallen.
When I saw the graph, the penny finally dropped for me.
The phrase 'jeden Groschen umdrehen' (to turn over every groschen/to watch every penny) means that you have to be very frugal and think carefully about every expense. Sometimes it is intensified with 'zweimal umdrehen' (to turn it over twice).
Während des Studiums musste ich jeden Groschen zweimal umdrehen.
During my studies, I had to watch every penny twice.
As a coin, the groschen is historical and is no longer used. This meaning appears almost only when talking about the time before the euro, often in a nostalgic tone.
Oma erzählt oft, dass ein Brot früher nur wenige Groschen gekostet hat.
Grandma often says that bread used to cost only a few groschen.
cent
'der Cent' and 'der Groschen' both have to do with small amounts of money. 'Cent' is a real currency unit today, for example one hundredth of a euro. 'Groschen' used to be a coin and today is usually no longer used as an exact amount of money. You are more likely to hear it in fixed expressions like 'jeden Groschen umdrehen' (to watch every penny) or 'der Groschen ist gefallen' (the penny has dropped). The words can be confused because both sound like small coins. For current prices and amounts, 'Cent' is correct; 'Groschen' fits better with older money or idioms.
Nach der dritten Erklärung ist bei Tom endlich der Groschen gefallen.
After the third explanation, the penny finally dropped for Tom.
An der Kasse fehlten mir noch zehn Cent.
At the checkout, I was still short ten cents.