You'll notice that alongside October, there's also November and December which should be the ninth and tenth months respectively. In the old Roman calendar, the months of July and August were originally known as Quintillus and Sextillus as well.

This was because in the old Roman calendar, the new year started on the 1st of March, with the beginning of Spring and the agricultural cycle. The change happens in 46BC when Gaius Julius Caesar becomes dictator of the Roman Republic and decides that the calendar is in urgent need of reform. In the new Julian Calendar, the New Year is pushed back to the 1st of January, thus pushing the month names out by a factor of two.