You pay a small premium upfront for the right — not the obligation — to buy a stock at a fixed price, any time before it expires.
An option gives the buyer the right, but not the obligation, to buy (a call) or sell (a put) a stock at a fixed price — the strike — on or before a set expiry date.
The buyer pays a premium upfront for that right; the seller (the "writer") collects the premium and takes on the obligation if the buyer chooses to exercise.
A buyer who thinks a stock is going higher can control 100 shares' worth of upside for a fraction of the price of owning them outright — and the most they can ever lose is the premium.
A seller who already owns the stock can sell calls against it to collect premium as income, effectively getting paid to agree to sell at a price they're happy with anyway.
Retail investors use options to speculate cheaply or to generate income against stock they hold; institutional desks use them to hedge portfolios against a sharp move.
Market makers quote both sides constantly, which is what keeps the whole options market liquid.