The letter "K" is used to represent 1000, because it represents the prefix "kilo," which means 1000 of something in the metric system. For instance, kilogram means 1000 grams.
The prefix "kilo" was taken from the Greek word chilioi or khilioi, which means thousand. This happened when a group of French scientists were commissioned to make the metric system. The metric system was designed to make conversions between units easier by making each unit a factor of 10 larger or smaller than the nearest units. Scientists needed to have standard prefixes that represented how much larger or smaller a specific unit was from the base unit. This makes it easy for a kilometer to be converted to a meter or a kilogram to a gram, because once the prefixes are known all conversions are standard.