On the topic of a visual understanding of how far 300 feet is, American football fields are an excellent place to begin. Try to picture one, as the entire field -- minus the zones at either end -- stretches a span of 300 feet. Of course, the field is divided by yards, but with one yard being exactly equal to three feet, both systems of measurement can be used interchangeably.
Three hundred feet is also a fairly standard measurement that comes up in everything from athletics and transportation, to the lengths of human production and human endurance. 300 feet is a common point of aspiration for would-be world record holders.
For example, in 2010 a man set a new world record by diving more than 300 ft below water on a single breath of air, with neither fins nor any other swimming aid to help him.
Recently, a group of people from San Antonio, Texas worked to create the world's largest enchilada, a 300 ft mammoth with a weight in excess of 3,100 lbs or 6,800 kg. Unfortunately, this incredible feat did not break any records as the enterprising chefs did not wrap their enchilada in a 300 foot tortilla. This is either a regretable lack of foresight, or an indication that the grocery store was fresh out of giant, giant, giant-sized tortillas.
Finally, an anonymous stunt driver will soon make an attempt to complete a world-record setting, 300 ft jump with his modified truck. This event will take place at the 2011 Indianapolis 500 as part of the celebration of its 100th anniversary.
There are more examples than these, but I'll stop here for now. Try to research some yourself!