Kushal's answer, although containing good information, can be a little misleading based on the context of your question.
The standard alpha value for text on a white background is 87% (#000000).
The quoted text you provide explicitly states that the percentages refer to alpha values.
I don't understand how these percentages work. For example, if the background color is white, what is the color of the text?
In this example the background is white (#FFFFFF) and the text is black (#000000). The alpha value of the text is 0.87.
What if my background were say #607D8B. What would my text color be? Is it just the background color with the opacity (alpha) set to the percentage?
That would be a blue-grey color, which in my opinion would fall under the "dark background" category. Use white text at full opacity.
Text opacity
Text may be displayed with different degrees of opacity to convey how important certain information is relative to other information. The level of opacity used for text depends on whether your background is darker or lighter.
Refer to this section of the guidelines for more detail.
Also, if you're choosing your colors from here, take note of what color font they use on top of it.