For reading to be comfortable there must be adequate contrast between the background and foreground. If the text is similar in brightness to the color behind it readers may still be able to make out the words, but doing so will strain their eyes and divert their attention away from the content.
The World Wide Web Consortium (W3C) has set standardized guidelines for the minimum contrast needed for text to be clearly legible on websites, and tools exist to test a given background/foreground combination for appropriateness. The W3C guidelines are designed with the visually impaired in mind, hoping to ensure that all text on websites can be understood even for those who cannot perceive subtle differences in shade (or those with old/defective displays that render colors at lower-than-intended contrast).
In addition to accessibility concerns about the legibility of text, color contrast is a vital element of readability because low-contrast text is significantly less comfortable to read for long periods of time. When styling long-form text, designers should carefully avoid the temptation to use light text on light backgrounds (or vise-versa).