A half-century is the term in cycling for riding at least 50 miles. The derivation is not a complicated thing to explain: a century is 100 miles, so a half-century is...half of that. A related term is a metric century, which is 100 kilometers, or around 60 miles.
The usage of the term "half-century" is not arbitrary, as 50 miles is an important landmark for cyclists. Under the entry for "century", it is stated that someone who can ride a bicycle can ride a century with a few months of training. I would say that while in some ways this is true, for most people a half-century is the more realistic target. While I would hardly call myself an expert on cycling, I do have one piece of advice that will explain distance cycling well, and is a starting point for cycling safety.
Over any distance more than about twenty miles, cardiovascular fitness is not what most cyclists have to worry about. If you can bicycle ten miles, you can probably bicycle a hundred, as far as aerobic capacity goes. On a small track, or on a flat, well-maintained route with regular sources of water, food and shade, a hundred miles presents no challenges. But the challenges of long distance cycling are other than the exercise required.
Other than the sheer exercise of it, the real challenges of cycling are weather (either too hot or too cold), water, food, soreness or cramping and mental fatigue. Picking an appropriate route is also a big part of riding a half-century in the real world, since the route should ideally have well-maintained roads that are relatively free of traffic, yet are close enough to populated areas that help can be reached in case of unforeseen circumstances.
That then, is why the metric century is a challenge, and a good goal for the casual long-distance cyclist. Riding a half-century requires more than the muscles to pedal, it requires carrying about a gallon of water, a few pounds of food, a change of clothing and a first aid kit. It also requires finding a place and time that is given for safe, and hopefully fun, riding. Often this means finding a time when there is enough sunlight to make riding easy, but not so much that heat exhaustion becomes a threat. Riding a half-century also requires taking regular rest breaks, since a day spent in one position can cause both the mind and body to become less responsive, which can be a very dangerous thing while riding.
So, while cycling a whole century (or further) might not be too difficult from the point of simple pedaling, logistics usually limits most cyclists to the more reasonable half-century.