"Proper following distances" means "you can react and stop in time to prevent a collision if the car in front of you brakes very hard".
Ripped from a wiki article on the topic:
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The United States National Safety Council suggests that a three-second rule—with increases of one second per factor of driving difficulty—is more appropriate. Factors that make driving more difficult include poor lighting conditions (dawn and dusk are the most common); inclement weather (ice, rain, snow, fog, etc.), adverse traffic mix (heavy vehicles, slow vehicles, impaired drivers, pedestrians, bicyclists, etc.), and personal condition (fatigue, sleepiness, drug-related loss of response time, distracting thoughts, etc.). For example, a fatigued driver piloting a car in rainy weather at dusk would do well to observe a six-second following distance, rather than the basic three-second gap."