The verbs erinnern and sich erinnern both mean "to remember." However, they are not interchangeable and are not the only verbs used to describe the act of remembering.

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Generally, the verb erinnern means to remind someone else, while the reflexive verb sich erinnern means to remember or recall something oneself. The preposition for both verbs is an, which is followed by the accusative.

Das Geräusch erinnert an das Summen einer Biene.

The sound is reminiscent of the buzz of a bee.

Caption 26, Deutsch mit Eylin: s, ß und ss

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Er erinnerte sie daran, dass man halten muss, was man verspricht.

He reminded her that you must keep what you have promised.

Caption 66, Märchen - Sagenhaft:Der Froschkönig

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Oh, ja, das stimmt. Ich erinnere mich an die Fotos, die du mir geschickt hast.

Oh yes, that's right. I remember the photos that you sent me.

Caption 21, Die Wohngemeinschaft: Besuch

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Other verbs can imply remembering as well. The phrase an etwas denken literally means "to think of," but can be used when you want to make sure that someone doesn't forget to do something, or be applied to past events: 

Denkt an die Tage, die hinter uns liegen.

Think of the days that lie behind us.

Caption 4, Andreas Bourani Auf uns

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The verb merken can be translated as "to notice" but also "to remember." 

So merkt man sich vieles noch viel besser.

That way, you'll remember many things much better.

Caption 57, Deutsch mit Eylin: Auf natürliche Weise Sprachen lernen mit Yabla

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An important distinction should be made between the nouns die Erinnerung and das Gedächtnis. While die Erinnerung refers to an individual memory or the act of remembering, das Gedächtnis is our general capacity to store information.

Peter Barsch geht es vor allem um die Erinnerung an eine Zeit, die man heute kaum noch verstehen kann.

What matters for Peter Barsch is, above all, the remembrance of a time that you can barely understand anymore today.

Captions 26-27, 25 Jahre Mauerfall: Radtour durch die Geschichte

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Jede Zeile von mir bleibt in deinem Gedächtnis.

Every line of mine will stay in your memory.

Caption 34, Nina Chuba: Wildberry Lillet Remix feat. Juju

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Further Learning
You'll find these nouns and verbs in many examples on Yabla German.

It's quite easy to make mistakes with German words that sound nearly the same but have different prefixes and thus different meanings. For example, some verbs using the root verb lassen (to let, to leave):

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Der Witzleben ist doch vor zwei Jahren vom Führer entlassen worden.

Witzleben was let go by the Führer two years ago.

Caption 23, Die Stunde der Offiziere - Dokudrama über den 20. Juli 1944 - Part 13

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Sie verlassen den amerikanischen Sektor, Berliner Mauer

You are leaving the American Sector, Berlin Wall

Caption 1, 25 Jahre Mauerfall - Radtour durch die Geschichte

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The verb entlassen can mean "to be fired" or "to be let go," but it can also mean "to be released" as in released from prison. Depending upon its context, the verb verlassen can mean "to leave" or "to abandon."

But what about German words with different prefixes that can be translated as the same word in English? It can be even more confusing to keep these straight. A very good example of this are the verbs heiraten and verheiraten.

Ich weiß, eines Tages, da heiraten wir.

I know someday we'll marry.

Caption 32, Monsters of Liedermaching - Für immer

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Using the example below with verheiraten and the subject reflected as the direct object (example 1: wir/uns, example 2: sie/sich), we arrive at the same meaning: 

Ich weiß, eines Tages, da verheiraten wir uns.
I know someday we'll marry.

Ich weiß, eines Tages, da verheiraten sie sich.
I know someday they'll marry.

Both of the examples could use "get married" instead of "marry". The verb verheiraten, when used without a reflective direct object, has a different meaning, however: 

Die Großmutter wollte den Sohn auf jeden Fall verheiraten.
The grandmother wanted badly to get her grandson married off. 

Another easily confused pair are geheiratet and verheiratet: 

Mein Bruder Martin hat letztes Jahr geheiratet.

My brother Martin got married last year.

Caption 19, Die Wohngemeinschaft - Besuch - Part 3

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Der König freute sich, dass seine Tochter endlich verheiratet war.

The King was delighted that his daughter finally got married.

Caption 37, Märchen - Sagenhaft - König Drosselbart

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Both geheiratet and verheiratet can be translated as "got married," but there's a big difference in how you use the words. The word geheiratet is a past participle of the verb heiraten. The word verheiratet, on the other hand, is an adjective which stems from the verb heiraten. Thus you can can say: Ich habe geheiratet ("I got married") or Ich bin verheiratet ("I am married") but not vice-versa! A good way to remember the difference is that the prefix ge- ist one of the most common prefixes used in past participles of German verbs. 

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Further Learning
Look for variations of heiraten and verheiraten on Yabla German to see them in a real-world context, and take a look at this article on the topic!