If the white light shines on an object and the object appears blue this means that?

That it's absorbing all the other colors but reflecting blue light. You see white light is actually a bunch of colors all together. When you see a rainbow it's just light being split to it's original components. For our eyes to see we need light to enter it. And we see color because an object is absorbing all the other colors and reflecting just one color light (in this case blue). The color light that is being reflected is the one that travels into our eyes allowing us to see color!