When newspaper journalist Henry Chadwick created the baseball recordkeeping system, he used the letter "K" to denote "strikeout" because he needed the letter "S" to communicate "sacrifice." He chose "K" because it was the last letter of the word "struck," a term which was more commonly used than strikeout in the early days of baseball.
While "K" denotes a strikeout in a scorebook, scorekeepers sometimes turn the "K" backwards to indicate that the batter struck out looking, whereas a normal "K" denotes that the player struck out swinging. Either way, the batter is out, but statisticians often like to know more detail about how a strikeout occurred.
While some scorekeepers have used "SO" to note a strikeout, this is sometimes confused with "shutout," the term used when a team scores no runs over the course of a game. The letter "K" is widely accepted by virtually all baseball scorekeepers as the universal sign for a strikeout.
In addition to being the first to use the letter "K" for strikeout, Chadwick was also the first to assign numbers to positions for scorekeeping. He is the reason why scorebooks refer to the pitcher as "1," the catcher "2," the first-baseman "3," etc.