das Gehör
hearing
The ability to perceive sound; one of the five senses of humans and many animals.
Im Alter lässt das Gehör oft nach.
Hearing often declines with age.

hearing
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hearing
The ability to perceive sound; one of the five senses of humans and many animals.
Im Alter lässt das Gehör oft nach.
Hearing often declines with age.

'Das Gehör' (hearing) is the noun corresponding to the verb 'hören' (to hear). The prefix 'Ge-' is often used to form an abstract noun from a verb, describing the ability or the result of the action.
Man braucht ein gutes Gehör, um alle Details in der Musik zu hören.
You need a good ear to hear all the details in the music.
When referring to the sense of hearing, 'Gehör' (hearing) is often combined with certain verbs and adjectives. You can 'ein gutes/schlechtes Gehör haben' (to have good/bad hearing) or 'sein Gehör verlieren' (to lose one's hearing).
Mein Großvater hat ein sehr gutes Gehör für sein Alter.
My grandfather has very good hearing for his age.
The expression 'sich Gehör verschaffen' (to make oneself heard) is reflexive and uses the dative: 'Ich verschaffe mir Gehör' (I make myself heard). It means actively making sure you are noticed and heard.
Die junge Politikerin konnte sich in der Debatte Gehör verschaffen.
The young politician was able to make herself heard in the debate.
The expression 'jemandem Gehör schenken' (to give someone a hearing) requires a dative object. The person you listen to is in the dative. It expresses that you give someone your full attention.
Der Psychologe schenkte den Problemen seiner Patientin Gehör.
The psychologist gave a hearing to his patient's problems.
The expression 'nach dem Gehör spielen' (to play by ear) is a fixed phrase. It means to play a piece of music without sheet music, only by remembering the melody one has heard.
Sie kann fast jedes Lied auf der Gitarre nach dem Gehör nachspielen.
She can play almost any song on the guitar by ear.
The expression 'ein feines Gehör für etwas haben' (to have a fine ear for something) is used metaphorically. It means to have a good feel or intuition for subtle details in a particular area.
Als Lektorin hat sie ein feines Gehör für sprachliche Fehler.
As an editor, she has a fine ear for linguistic errors.
attention
'die Aufmerksamkeit' and 'das Gehör' can both have to do with someone being noticed or heard. 'Aufmerksamkeit' is more general: you concentrate on a person, a thing, or an activity. 'Gehör' actually means the ability to hear, but it is used differently in fixed expressions. 'Jemandem Gehör schenken' means to listen to someone attentively. 'Sich Gehör verschaffen' means to make sure that others listen. Learners may confuse the words because both can be connected with listening. For concentration in general, 'Aufmerksamkeit' fits; in these fixed expressions, 'Gehör' fits.

Die Mitarbeiter haben dem Kunden Gehör geschenkt und seine Beschwerde ernst genommen.
The employees listened to the customer and took his complaint seriously.
Vor dem Termin braucht Mehmet Ruhe, damit seine Aufmerksamkeit nicht nachlässt.
Before the appointment, Mehmet needs quiet so that his attention does not fade.