Learn Dutch: Je moet fietsen om je conditie te verbeteren. - You must cycle to improve your stamina.

om ... te translates to "in order to". It shows the purpose of an action. You put om at the beginning of the purpose phrase, and te right before the infinitive verb at the very end. So, om je conditie te verbeteren literally means "in order your stamina to improve".

Could I say "voor je conditie verbeteren" instead, like "for improving" in English?

No, Dutch doesn't use voor (for) with a verb to express purpose. When you want to say "to [do something]" or "for [doing something]", you must use the om ... te + infinitive structure.

Does conditie mean the same thing as the English word "condition"?

Often, yes, but in the context of health and sports, conditie specifically means "stamina" or "fitness". If a Dutch person says they have een goede conditie, it means they are in great physical shape and have high endurance.

Why are there two verbs, fietsen and verbeteren, at the end of their respective phrases?

The first part of the sentence uses the modal verb moet (must), which pushes the main verb fietsen (to cycle) to the end of its clause. Then a new purpose clause starts with om. In an om ... te clause, the infinitive verb (verbeteren) always goes at the very end.