auffallen
to stand out
To attract attention, to be noticed, often because of a special feature or behavior.
Mit ihrem roten Mantel fällt sie in der Menge sofort auf.
With her red coat, she immediately stands out in the crowd.

to stand out / to notice
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to stand out
To attract attention, to be noticed, often because of a special feature or behavior.
Mit ihrem roten Mantel fällt sie in der Menge sofort auf.
With her red coat, she immediately stands out in the crowd.

'Auffallen' (to stand out / to notice) is a separable verb. The prefix 'auf' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Sein neues Auto fällt sofort auf.
His new car stands out immediately.
This verb is very often used with a person in the dative to express who notices something. The structure is: [person in the dative] fällt [thing in the nominative] auf.
Mir ist seine neue Frisur sofort aufgefallen.
I noticed his new hairstyle immediately.
To evaluate how something stands out, the verb is often combined with adverbs such as 'positiv' (positively), 'negativ' (negatively), 'angenehm' (pleasantly), or 'unangenehm' (unpleasantly).
Seine laute Stimme fällt im Büro unangenehm auf.
His loud voice stands out unpleasantly in the office.
When you notice that a particular situation is the case, the structure 'Mir fällt auf, dass ...' (I notice that ...) is often used. What you notice is described in a subordinate clause with 'dass' (that).
Mir ist aufgefallen, dass du in letzter Zeit sehr müde wirkst.
I noticed that you have seemed very tired lately.
background
'sich im Hintergrund halten' (to stay in the background) and 'auffallen' (to stand out) describe opposite behaviors. Someone who 'sich im Hintergrund hält' deliberately remains inconspicuous and draws little attention to themselves. Someone who 'auffällt' is noticed, often because of special behavior, appearance, or achievement. So the contrast is: not wanting to be the center of attention, or being clearly noticed. This difference is especially important in social situations.

Mit ihrem roten Mantel fiel Anna sofort auf.
With her red coat, Anna stood out immediately.
Bei der Feier hielt sich Tom lieber im Hintergrund.
At the party, Tom preferred to stay in the background.