Learn Danish: Hun er altid aktiv for at forbedre konditionen. - She is always active to improve her fitness.

In English, we often just use "to" when we mean "in order to". But in Danish, when you are expressing the purpose of an action, you must use for at before the infinitive verb. If you just used at forbedre, it would sound grammatically incomplete.

The English translation says "her fitness", but the Danish sentence uses konditionen. Where is the word for "her"?

Konditionen literally means "the fitness". In Danish, when talking about something intrinsically linked to a person, like their body, clothes, or physical condition, you usually use the definite ending instead of a possessive pronoun like hendes (her). Because it is obvious it is her own fitness she is improving, the definite form is all you need.

Does kondition mean general health and fitness?

It specifically refers to cardiovascular fitness, endurance, or stamina. If she were lifting weights to get stronger, you would more likely talk about her styrke (strength). When Danes say someone has good kondition (often shortened to kondi), they mean the person can run or cycle a long way without getting out of breath.

Why does altid come after the verb er?

Altid (always) is a central adverb. In a normal main clause where the subject comes first, these adverbs always go immediately after the first verb. That is why it is Hun er altid and not Hun altid er.