Binary options brokers will generally have their trading platform open when the market of the underlying asset is open. So if trading the NYSE, Nasdaq, DOW or S&P, the assets will be open to trade during the same hours as those markets are open. Any moves by the Federal reserve for example, will feed into binary markets immediately, just as you would expect.
A binary option is a financial exotic option in which the payoff is either some fixed monetary amount or nothing at all. The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The former pays some fixed amount of cash if the option expires in-the-money while the latter pays the value of the underlying security. They are also called all-or-nothing options, digital options (more common in forex/interest rate markets), and fixed return options (FROs) (on the American Stock Exchange).