The German language actually has two words for “memory”. One is Gedächtnis and can be defined as the collection of knowledge about the past, and the other is Erinnerung which refers to the retrieval and mental reproduction of past impressions. To put it a different way, Gedächtnis is like a hard drive, and Erinnerung is like the act of opening a file.
Also, Gedächtnis usually refers to hard facts and concrete data that one has memorized (such as the population density of Bejing), whereas Erinnerung is less specific (the memory of one’s first kiss for example):
Er kann Fakten gut im Gedächtnis behalten. He’s good at keeping facts in his memory.
Das weckt in mir Erinnerungen. That awakens memories in me.
The good news is that the English word “remember” and “remind” are both summed up neatly in only one word in German – erinnern:
Erinnere mich noch einmal. Remind me again.
Ich erinnere mich nicht. I don’t remember.