die Gesundheit
health
The state of physical, mental, and social well-being; the absence of illness or infirmity.
Regelmäßiger Sport ist wichtig für die Gesundheit.
Regular exercise is important for health.

health
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health
The state of physical, mental, and social well-being; the absence of illness or infirmity.
Regelmäßiger Sport ist wichtig für die Gesundheit.
Regular exercise is important for health.

The noun 'Gesundheit' (health) is derived from the adjective 'gesund' (healthy) with the ending '-heit'. This pattern is often used to form abstract nouns from adjectives.
Freiheit, Schönheit und Gesundheit sind wichtige Güter im Leben.
Freedom, beauty, and health are important things in life.
As an exclamation ('Gesundheit!' — bless you/cheers), it is a reaction to someone sneezing or a toast. In a sentence structure, it refers to physical or mental condition.
Als sein Kollege nieste, sagte er sofort: „Gesundheit!“
When his colleague sneezed, he immediately said, "Bless you!"
Common verbs related to the state of health are 'auf die Gesundheit achten' (to pay attention to one's health), 'die Gesundheit schädigen' (to damage health), 'die Gesundheit fördern' (to promote health), or 'vor Gesundheit strotzen' (to be bursting with health).
Rauchen kann die Gesundheit ernsthaft schädigen.
Smoking can seriously damage your health.
When someone sneezes, it is a polite and very common custom in Germany to say 'Gesundheit!' (bless you) to wish the person well.
„Hatschi!“ – „Gesundheit!“
"Achoo!" — "Bless you!"
illness / disease
'die Gesundheit' and 'die Krankheit' are clear opposites. 'Gesundheit' describes a good physical or mental state. 'Krankheit' describes a state in which health is impaired, or a specific illness or disease. For example, people talk about good health when someone feels well and is not sick. People talk about illness when someone has symptoms, needs treatment, or is absent because of it. This is not about the exclamation 'Gesundheit!' when toasting or after someone sneezes, but about a person's state of health.

Regelmäßige Bewegung ist gut für die Gesundheit.
Regular exercise is good for your health.
Wegen seiner Krankheit bleibt Tom heute zu Hause.
Because of his illness, Tom is staying home today.