
die Betätigung
activity
An activity or occupation that one engages in, often to challenge or occupy oneself physically or mentally.
Regelmäßige sportliche Betätigung ist wichtig für die Gesundheit.
Regular physical activity is important for health.
activity / operation
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activity
An activity or occupation that one engages in, often to challenge or occupy oneself physically or mentally.
Regelmäßige sportliche Betätigung ist wichtig für die Gesundheit.
Regular physical activity is important for health.

operation
The starting or operating of a technical device, switch, or mechanism.
Die Betätigung des Not-Aus-Schalters stoppt die Maschine sofort.
Operation of the emergency stop switch stops the machine immediately.
The word is derived from the verb 'betätigen' (to operate / to be active). This verb means to be active ('sich betätigen') or to operate something ('einen Schalter betätigen' — to operate a switch). The ending '-ung' turns the verb into a noun.
Er betätigt sich gerne im Garten.
He likes to be active in the garden.
You can recognize the meaning from the context. If it is about people and their activities (often with adjectives like 'sportlich' — athletic/sporting — or 'künstlerisch' — artistic), it means an activity. If it is about technical devices (such as 'Schalter' — switch, 'Hebel' — lever, 'Bremse' — brake), it means operating something.
Künstlerische Betätigung kann sehr entspannend sein.
Artistic activity can be very relaxing.
When referring to an activity, 'Betätigung' (activity) is often combined with adjectives that describe the type of activity. Common examples are 'körperliche Betätigung' (physical activity), 'geistige Betätigung' (mental activity), and 'sportliche Betätigung' (athletic activity).
Ärzte empfehlen mindestens 30 Minuten körperliche Betätigung pro Tag.
Doctors recommend at least 30 minutes of physical activity per day.
To express what is being operated, the genitive is used very frequently. This structure sounds formal and is common in technical instructions.
Die versehentliche Betätigung des Alarms löste einen Feuerwehreinsatz aus.
The accidental operation of the alarm triggered a fire department response.
movement
Bewegung and Betätigung can both refer to physical activity for balance and well-being. Bewegung emphasizes moving the body more strongly, while Betätigung refers more generally to a physical activity or occupation. When talking about physical movement itself, Bewegung is more suitable; when referring to an activity one engages in, Betätigung is often more precise.

Gartenarbeit ist für meine Mutter eine angenehme körperliche Betätigung.
Gardening is a pleasant form of physical activity for my mother.
Regelmäßige Bewegung hilft mir, nach einem langen Arbeitstag gesund zu bleiben.
Regular exercise helps me stay healthy after a long day at work.