An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a set price by a set date. The buyer pays a premium for that right.
There are two types. A call option carries the right to buy the underlying at the strike price, and a put option carries the right to sell it at the strike price. The underlying can be a stock, index, ETF, commodity, currency, or futures contract.
An option is one kind of derivative, not the whole category. Every derivative takes its value from an underlying asset, but an option is the type that grants a right rather than an obligation. A futures contract, by contrast, obliges both sides to transact, whereas an option buyer can let the contract expire if exercising it is not worthwhile.
You buy a call option on a stock with a USD 50 strike price.
The stock later rises to USD 60 before the option expires.
The call has value because you can buy at USD 50 while the market trades at USD 60:
USD 60 - USD 50 = USD 10 per share
That USD 10 per share is the gain before you subtract the premium you paid for the option.