As a noun, it is an extra amount of money you pay for something better or for insurance. As an adjective, it describes something of higher quality that usually costs more.
From Latin *praemium* meaning 'reward' or 'prize'. Over time, English shifted the idea from a reward you receive to an extra amount you pay, especially for better quality or insurance.
A 'premium' started as a reward you got, not something you paid. Language flipped it: now you pay a premium to get a reward in quality or protection. The word still quietly carries the idea of a special bonus.
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