If you enable this option, then the parts making up the individual questions will be randomly shuffled each time a student starts an attempt at this quiz, provided the option is also enabled in the question settings.
The intention is simply to make it a little harder for students to copy from each other.
This only applies to questions that have multiple parts, such as Multiple Choice or Matching Questions. For multiple choice questions the order of the answers is shuffled only when this option is set to "Yes". For matching type questions the answers are always shuffled, this setting controls whether in addition the order of the question-answer pairs is shuffled.
This option is not related to the use of Random Questions.