A binary option is a type of options in which your profit/loss depends entirely on the outcome of a yes/no market proposition: a binary options trader will either make a fixed profit or a fixed loss.
An option chain is a comprehensive list that shows you all available option contracts for a given stock. These are sorted by their expiration date, which is the last day you can trade or use the option, and strike price, which is the price at which you can buy (call) or sell (put) the stock.