HQHD-Day occurred on August 6th, 2015.
HQHD-Day is the name of the day that the Smash 4 Social Thread 6.0 was locked down for a little less than 24 hours, out of request/demand by Admin Hylian to increase the quality of the posts left in the thread.
The thread was locked down on page 1080, similar to the higher pixel quality 1080p.
Hylian's post described the need for higher quality posts, and was posted on page 1080. Thus, this day was dubbed HQHD-Day, as a reference to the coincidental occurrence of the event.