FR is the most important thing for tonal perception which is 99% of headphone sound. If you really get into it, is actually the only thing that matters. Most people say FR to refer to a graph someone posts. That graph that you see can give you an idea of the tonal balance with the conditions it was measured on (hopefully a good seal on an average pinna with a specific acoustic impedance).

In reality, what you hear will be different. Some headphones will interact with your ear better than other headphones, some headphones will have peaks and dips where you would normally hear peaks and dips and that would make the headphone sound wider or more natural than another headphone. The HD800/s have an upper mid dip that makes music sound further away along with excellent pinna interaction. This makes the headphone sound wide and naturally so. Rtings has a measurement for this but it doesn't necessarily tell the whole story every time but I've yet to see a better method.

Your ears alter the FR of everything you listen to. Things in front of you have a dip around 8-10kHz because the high frequency waves bounce off the ridges in your ear and cancel out around that frequency. A headphone that either has a dip where you have or interacts with your ear to make that dip naturally would sound more in front. Image example of what I'm talking about here.

Some headphones also are super hard to seal on anyone's head. If the headphone was measured on a head simulator with a good seal and it seals on your head very poorly, what you hear will be dramatically different from what was measured. Closed back and DCA open back headphones are notorious for this. There are some other headphones, like most Hifiman and the Meze Empyrean that are designed so that they don't have such a big change with a break in the seal, often times getting a small boost follow by roll off below the driver's resonance frequency. Examples: DCA, Meze, Hifiman.

All of these things are FR but not what you see on most FR graphs. Distortion affects FR, soundstage comes from FR, the natural feeling of a headphone comes from FR, it just isn't something you can point to on the usual graph and say "that's soundstage" because it is often different for each person the headphone is put on. You can see how a headphone interacts with the measurement fixture to see if it is just the innate peaks and dips of the headphone making it seem that way to one person or actual interaction with the measurement rig's ears. This requires multiple measurements most of the time and isn't normally shown with a regular FR graph.

Hearing is fairly well understood and is the effect of pressure at certain frequencies on your ear's sensory parts. The measurement of this pressure at a given frequency is what a FR graph is and why it is generally the main important part of a headphone but you have to understand what the graph means, what it can tell you, and what it can't tell you. Often times You pretty much always need much more than just one measurement though.

Why we perceive these things are also fairly well understood and I have a playlist of really nice lectures if you are genuinely interested in learning. It is some really cool stuff.