Status registers are exactly what the name insinuates, registers that dictate status. They're bloody flags. Each processor has a set of 'em which can be interrogated by machine language instructions. Ordinarily they're single binary digits and a number of status registers will be contained within a single register of, guess how many, yes, the magic number, 8 binary digits.

Examples would include the carry flag, which is set if the addition of two digits causes a carry and a zero flag is set if the compare instruction or arithmetic operation just executed gives a zero result.