
sich erinnern an
to remember
To recall information or an experience from memory.
Ich kann mich gut an unseren ersten gemeinsamen Urlaub erinnern.
I can remember our first vacation together well.
to remember / remind
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to remember
To recall information or an experience from memory.
Ich kann mich gut an unseren ersten gemeinsamen Urlaub erinnern.
I can remember our first vacation together well.

to remind someone
To draw someone's attention to something that he or she may have forgotten.
Kannst du mich bitte daran erinnern, dass ich noch die Blumen gießen muss?
Can you please remind me that I still have to water the flowers?

to be reminiscent of
To have a similarity to someone or something, so that seeing it makes you think of that person or thing.
Dieses Gebäude erinnert stark an eine alte römische Villa.
This building is strongly reminiscent of an old Roman villa.
The structure of the sentence determines the meaning. 'Sich erinnern' (to remember, reflexive) means to recall one's own memory. 'Jemanden erinnern' (to remind someone, non-reflexive, with an object) means to help another person remember.
Ich erinnere mich an meine Kindheit.
I remember my childhood.
In all its main meanings, 'erinnern' (to remember/remind) is fixed with the preposition 'an' and the accusative. A common mistake is using the wrong case or a different preposition.
Erinnerst du dich noch an das Lied?
Do you still remember the song?
When the subject of the sentence is a thing, a place, or a smell, 'erinnern an' (to be reminiscent of / to remind someone of) means that it has a similarity to something else. In this case, the verb is not reflexive.
Dieses Parfüm erinnert mich an den Sommer in Italien.
This perfume reminds me of summer in Italy.
to remind / warn
Erinnern neutrally refers to a possibly forgotten obligation. Mahnen is more forceful and is used especially for payments and debts that are due or already overdue. Before the payment deadline, you can send a friendly reminder; after a default, you can formally mahnen the debtor.

Die Firma erinnert den Kunden freundlich an die Rechnung, die nächste Woche fällig wird.
The company kindly reminds the customer about the invoice, which is due next week.
Die Firma mahnt den Kunden schriftlich, weil die Rechnung seit zwei Wochen überfällig ist.
The company sends the customer a written payment demand because the invoice is two weeks overdue.