The word soccer was first used in the 19th century in England and started out as a short form for the term 'Association football'. There is a popular story that the term was originally coined by an Oxford scholar and footballer called Charles Wreford Brown, who liked using short slang terms such as 'brekker' for breakfast. However, there is no real evidence for this and it is likely that the term just developed naturally, as abbreviations tend to.
Association Football means football played according to the rules of the Football Association or FA, which was founded in England in 1863. Football in various forms had been played for hundreds of years and in many countries before that, but the FA began the process of making it an official and regulated sport. The FA's rules themselves go back earlier, to the Cambridge Rules which were established in 1848, with input from several public schools.