Harry Potter fan's pet-form (if you will) of Lord Voldemort, the villian of the series. Used in refering to the Dark Lord in a casual or capricious way, which we can do because we're not terrified of him like the wizarding world of the books is (no wizard in the books would dare utter the name "Voldy", because it would be the rough equivalent of calling Hitler "Hitley" or something---basically, it just wouldn't fly). Also probably used because "Voldy" is a lot shorter than "Voldemort".
Then we discover that he could have possibly been in Harry's place if Voldy would have marked him instead of Harry.
Being fearful of naming someone or something. The phrase takes cue from the line associated with "Lord Voldemort" in the Harry Potter series: 'he who must not be named'.
The phrase was coined by British activist Maajid Nawaz in context of Islamism; analysts being fearful or reluctant to call out the ideology of Islamism as the underlying cause of Jihadist terrorism.
Left-liberals often succumb to the Voldemort Effect when discussing Islamic terrorism.