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
Loading your saved state.
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.

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.
activity / occupation
'die Tätigkeit' and 'die Betätigung' can both mean an activity that someone engages in. 'Tätigkeit' is more neutral and is very often used for tasks, work, or individual activities. 'Betätigung' sounds somewhat more formal and is especially suitable when talking about physical, mental, or creative activity. For example, you say 'sportliche Betätigung' (physical activity / exercise) when you mean in general that someone is moving their body. In everyday language, 'Tätigkeit' is usually more normal, while 'Betätigung' often appears in somewhat more elevated or factual texts.

Regelmäßige sportliche Betätigung hilft ihm, nach der Arbeit abzuschalten.
Regular physical activity helps him unwind after work.
Im Gespräch erklärt die Mitarbeiterin ihre neue Tätigkeit im Team.
In the conversation, the employee explains her new role on the team.