Bungie introduced a few puzzles to Destiny 2 with The Witch Queen and completing one of them is required to start the Altar of Reflection properly.
Puzzles in Destiny 2 range from easy to community-wide efforts across several weeks and there is a ton of brain teasers along the way. These are great enjoyment on their own but they don't work properly in some cases, like with Altar of Reflection. Here is a quick rundown on how to start the quest if you're having trouble.
Altar of Reflection: Catalyst has you going to a Deepsight node which reveals fluorescent markings when activated. It's clear you have to do something with them but even if you found the solution, it's possible the quest didn't progress.
The solution is simple - you have to stand in the right place, with a point of view from which the markings form the Witch Queen symbol, as is shown in the image below.
In some cases, simply lining up the solution properly will progress the quest. If it doesn't, make sure you are standing in the same spot as in the picture above and then jump once, without activating any of the movement abilities like Double Jump or Lift.
The jump activated the quest progress for me and a portal that looks like a mirror showed up shortly after.
Proceed through the portal and complete the rest of the mission, which is not particularly hard.