You could think of a commonly used representation of chance: There's a bag with some blue balls and some red balls. You reach into the bag and randomly take out one of the balls. You may get a blue ball, or you may get a red ball. You have (in an ideal situation) no way of knowing which it will be beforehand.
To further emphasize that you can't know beforehand which color the ball will be, and that you can't influence which color it will be, the person drawing the ball is often described as blinded. The person may close their eyes, or the person may wear a blindfold, or something similar. Human beings take a huge portion of the information about their surroundings from sight. If you take that away, you basically take away most of the danger that the supposedly random drawing of a ball will be skewed in any way.
So, it's a commonly used verbal image to further emphasize chance or randomness by describing it as "blind". It's not just "ordinary randomness", so to speak, but pure and utter randomness - or "blind chance".