I'm not sure if we can avoid going back to Aristoteles here

And forget the "martial"-part for a moment.
Aristoteles said art was based on imitation: depending on what kind of person we imitate we'll get tragedy (imitating a "majestic" character) or comedy (imitating a "low fellow" character) as a result.
The whole history of art of course coloured and detailed this much further but I still find this essential.
Martial art looks no different to me when it comes to forms - there's always something to imitate: depending on the level of abstraction it can be something concrete (like an animal, just think about the shaolin forms), it can be something semi-conceptual thing based on the material world (like the element-forms in Japanese martial arts) and it can be something fully conceptional (like the Wing Chun forms and a lot of dance styles. Yes, a dance is a form for me

).
Although they look really different, they all have one thing in common: the imitation. The slider between the far ends of the line between "material" and "conceptual" can be anywhere really, as long as it serves its purpose, it's complete in its own terms and delivers a certain experience I consider it a form.
From here it can be a very interesting discussion on the symbols and rituals of the forms: how the human mind connects to a certain "sacred" semantic field when the moves are carried out, how the whole form transforms the person who does it, how many times an orchestra has to practice the musical concept together until it really sings one time and only for a few minutes in which experience all the musicians' personalities melt into a symbiotic wholeness, how in an unexpected moment the tango dancers give up their lead and let the dance dance them rather than they dance the tango...
When I grab a lightsaber from the rack I do it because I pursue something like this. Something sacred. And if I can let go of everything else but me and the saber then I have the chance to access something really delicate and wonderful. If the form is suitable for me it can lead me deep down to the rabbit hole.
Funny thing but my first experience like this in martial arts was about 15 years ago and it wasn't a whole form but only a single stance. Typical story, we trained the basic horse stance in shaolin kung fu (ma pu) and there was a moment when I just "clicked" and felt that enormous depth and rooted myself into it. It was a few moments only but it was enough to open this door so I could try to evoke it again and again. The Earth lightsaber form I created for example is based on this experience: I chose moves based on this semi-concept of a tree rooted deeply and safely into the ground and while all the moves up at the "branches" are to tear the structure apart, the roots are much stronger and solid enough to define the strength and keep the form together.
It "sings" to me because it's a complete revival of that very first experience of rootedness and maybe sings for a few others who had a same sort of experience or at least they are seeking for something like it. And it's surely an empty shell for others.
So in other words a form is an offer. A possibility, a door wide open, a structure in which one can experience something wonderful.
I know a lot of martial artists compare the forms based on their "effectiveness" over the other or over a situation based on assumptions. For me a form is much more than just effective techniques listed one after the other, it's rather an invitation to try myself in a certain shape, in a certain way, in a certain context. Just like music or dance