A put gains value when the underlying falls. Buyers use puts as a bearish bet or as insurance on stock they own (protective-put). Sellers collect premium and agree to buy shares at the strike-price if assigned (cash-secured-put).
Puts on indexes are the main way portfolios are hedged, which is why put demand drives implied-volatility higher in selloffs.
Example: a stock is $50. You buy a $45 put for $1.00 ($100). If the stock falls to $38 by expiration the put is worth $7, a $600 profit. If it stays above $45 you lose $100.
Related: call-option, protective-put, cash-secured-put, strike-price