A spectral line is a special key frequency that can unlock and electron in an atom and cause it to move to a higher energy level. Several thousands of these lines are known. The authors made a bar chart that showed how many spectral lines were known for each frequency. They found that the shape of the bar chart looked like the shape of the spectrum of the light that would be emitted by a glowing stove element at 9000K (admittedly this would vaporize the stove element but just imagine the red-orange-yellow-white thing extended a bit further). The "spectrum" of the light means a chart of how bright each color of the rainbow would be if you made a rainbow out of the light by diffracting it through a prism. (For example, if I made a rainbow out of an Edison lightbulb's light, the blue and purple part of that rainbow would be much dimmer than if I made a rainbow out of sunlight.)

There is no particular relationship known between these two things. The authors are curious about why the charts look the same. The authors forgot to pull the old trick where you publish your speculation separately from your experimental results[0], so HN is complaining about their speculation.

[0] The trick works because physicists are mainly interested in remembering right answers, so if your speculations are wrong they will remember only the experiment, and if your speculations are right they will remember both.