The buyer of the put option has the right, but not an obligation, to buy the underlying asset at the strike price at expiry. The buyer of a put option has to pay a premium to the seller for the privilege.
The seller of the put option has an obligation to buy the underlying asset at the strike price if the buyer chooses to execute his right. The seller receives a premium from the buyer.
The buyer of the call option has the right, but not an obligation, to buy the underlying asset at the strike price at expiry. The buyer of a call option has to pay a ‘Premium’ to the seller for the privilege.