First and foremost, love of Star Wars has drawn me to saber combat, so pretty much since I was five years old. The classic saber hums, clashes, and activation/deactivation sounds always put a grin on my face.
Beyond that, a friend of mine who happens to be both a history buff and a Star wars fan, drew me in by pointing out the similarities between saber styles and real world sword/fencing techniques. I found it very fascinating how the techniques of various styles are employed, both in the Star Wars universe and historical context, whether it be breaking enemy lines or pinpoint precision. Hope to get past Shii-Cho one day, just need to figure out this orbit, and I feel like I can move on, maybe Makashi! If I can figure out all their real-world counterparts, maybe I will study these styles.
Additionally, the finesse, athleticism, intensity, and elegance, hard not to be impressed by all of that. Also the emotional regulation, states of mind one must place themselves in, planning your next move, guessing/predicting your opponent's, there's a certain thrill to it, especially when you emerge victorious. I'm no martial artist, but I won't let that stop me from learning!
I also like the symbolism of it as well, as it has become the one of strongest identifying characteristics of Sith, Jedi, and Gray Jedi, to the point where it is nearly a fault *insert KOTOR II quote here about how lightsabers don't truly define force sensitives* .]
Lastly, the overall experience of saber combat. Went to a big old saber clash last year in San Diego, Jedi vs Sith, and, needless to say, was awesome. Seeing so many people of differing ages, races, skill level with sabers, etc., all united by one thing, their love of swinging a saber at the other person! Not to mention, there was sort camaraderie between opponents, having heard the occasional "good duel" and "crap! are you alright!?". Swung my saber until my body grew heavy, and even then, still kept going until the girlfriend physically dragged me out! Very cathartic, if I may add. With that, I'm always eager for a good saber spar!