You may sometimes hear/read it said that Muslims time the night prayers by "when it gets so dark, you can't tell a white thread from a black thread". Similar statements are made about other matters of timing. This is wrong on multiple levels.
The verse in the Qurʼān  that is being massively misinterpreted does not say how to tell when twilight ends, but when dawn begins. Oh, for those of you who think dawn = sunrise - - - NO! Dawn is the time of increasing light before sunrise, just as twilight is the time of decreasing light after sunset. I don't care how many people misuse dawn to mean sunrise; this misuse is based on the gabblings of politicians and advertizers, and completely incorrect.
Anyway---The verse in the Qurʼān refers to the beginning of dawn, specifically the time, each day, in Ramaḍān, when the fast begins. It does not, directly, have anything to do with the time of prayer, as it refers specifically to the Ramaḍān fast. However, it has been taken as a guide for the proper time of two of the five required prayers.
BUT! it doesn't mean to hold up a couple of pieces of thread and see if you can distinguish between them. The "threads" are metaphorical. Indeed, the most scholarly translations refer to the white "smear," the white "line," the white "streak" of dawn, etc.; as well, they refer to "the blackness of night," "the darkness of night," the "black streak", etc. That is, it speaks of when you can tell the first light of dawn, which shows first as a line along the horizen, from the black of night. That's when the strictures of the Ramaḍān fast start to apply for that day.
A word for word translation is:
"And eat and drink until becomes distinct to you the thread [the] white from the thread [the] black of [the] dawn." 
Note that it is "OF the dawn" not "at the dawn". Clearly, the white and black "threads" are part of the dawn, and are metaphorical. No-one is expected to walk around with a couple of threads in their pocket and hold them up now and then; that image is misleading and insulting, and perhaps was always meant (by anti-Islam westerners) to be insulting.
You may be wondering what is done if the moon is bright, or the horizen is all clouded over, or near a large city or other source of light pollution. Simple: by most scholars of sharīʻa it is assumed that when the sun is X degrees below the horizen, that is the start (or end) of the white streak. How much X is varies according to different interpretations, but the idea is widely accepted.
Now I hope you understand the real meaning of "tell a white thread from a black."