An option is a contract giving you the right (but not the obligation) to buy or sell a stock at a fixed price by a certain date. A call lets you buy; a put lets you sell.
In 1973, Fischer Black and Myron Scholes published a formula that calculates the fair price of such a contract based on the current stock price, strike price, time to expiry, interest rate, and expected volatility. They won a Nobel Prize for it. This tool implements that formula — entirely in your browser.