die Krankheit
illness / disease
A condition in which physical or mental health is impaired; a specific disease or ailment.
Die Grippe ist eine weit verbreitete Krankheit im Winter.
The flu is a widespread illness in winter.

illness / disease
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illness / disease
A condition in which physical or mental health is impaired; a specific disease or ailment.
Die Grippe ist eine weit verbreitete Krankheit im Winter.
The flu is a widespread illness in winter.

'Krankheit' (illness/disease) is derived from the adjective 'krank' (sick/ill). The ending '-heit' forms abstract nouns from adjectives that describe a state, as also in 'frei' (free) → 'Freiheit' (freedom).
Nach langer Krankheit fühlt er sich endlich wieder besser.
After a long illness, he finally feels better again.
To describe an illness in more detail, adjectives such as 'schwer' (severe), 'ernst' (serious), 'chronisch' (chronic), 'ansteckend' (contagious), or 'selten' (rare) are often used.
Er leidet an einer seltenen, chronischen Krankheit.
He suffers from a rare, chronic illness.
You 'hat' (have) or 'bekommt' (get) a disease/illness. If you suffer from it, you use the fixed expression 'an einer Krankheit leiden' (to suffer from an illness/disease, with dative).
Viele Menschen im Büro haben die Grippe bekommen.
Many people in the office have caught the flu.
When 'Krankheit' (illness) serves as a general reason for an absence, it is often used with the preposition 'wegen' (because of/due to). In this case, no specific illness is named.
Das Geschäft bleibt heute wegen Krankheit geschlossen.
The shop is closed today due to illness.
health
'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.

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