When you walk into a room where light is low, your eye adjusts in several ways. First, the rod and cone cells on the retina begin to produce more light-sensitive chemicals. These chemicals detect light, convert it to an electrical signal and transmit that signal to the brain. Second, the iris muscles relax, which causes the opening of your eye, the pupil, to become very large. This allows your eye to collect as much light as possible. Finally, the nerve cells in the retina adapt so that they can work in low light. When you read, your eye must be able to focus an image of the words onto your retina. To do this, the iris, as well as the muscles that control the shape of your lens, must contract to keep the focused image on the retina.
If you read in low light, your visual muscles get mixed signals: Relax to collect the most light, but at the same time, contract to maintain the focused image. When that object is poorly lit, focusing becomes even more difficult because the contrast between the words and the page isn't as great, which decreases the eye's ability to distinguish visual detail. That ability is called visual acuity. Your eyes have to work harder to separate the words from the page, which strains your eye muscles.
When your eyes are working this hard for a long period of time, they become tired, much as any muscle would. The strain may result in a number of physical effects including sore or itching eyeballs, headaches, back and neck aches and blurred vision. Because you often don't blink enough when focusing on a single object, you may also experience uncomfortable dryness in your eyes. None of these symptoms damage your eyes, and they eventually go away. If the symptoms don't go away once you stop straining your eyes, however, then see an eye doctor. You may have an underlying eye problem like nearsightedness; the fact that the symptoms of eye strain overlap with those of nearsightedness is likely a reason why some continue to argue that reading in dim light causes permanent damage.
For now, it seems, the eyesight of children who read by flashlight is safe. Still, it's certainly easier on your eyes to read in good light that falls directly on the page without causing a glare. You can also avoid eye strain when you're reading by blinking frequently and taking a moment to focus on something out the window or across the room every 15 to 30 minutes.