So, what's appealing about Planescape? If I was to sell this to average D&D Dan and tell them what Planescape may offer them as a unique campaign setting, I might say that three major selling points of Planescape could include…
1. Fantasy Taken to the Edge
Planescape is not traditional fantasy. It is extreme and hyperbolic. When at its most iconic, it is not about elves and dwarves and hobbits and dragons and wizards, it is about Truth and Justice and Utopia and big, unanswerable, infinite questions like "What is the best way to live?" or "What is true in this subjective world?" or "Is War Good?" Its spellpunk grit and limitless protential variety serve this by simultaneously allowing for a high level of wahoo weirdness, but putting it in context as exploring those big questions. You, too, can play a free-willed intelligent sword strapped to the back of a particularly loyal golden retriever as a PC, if you want, but you play that character in context as seeking to answer the unanswerable questions that might arise from their life — what is good? What is bad? What is truth? What is the right way to be? Even the weirdest characters are pushed beyond their extremes in Planescape.
2. Infinite Perspectives
Planescape, when it is at its most iconic, is not a setting about Good Guys vs. Bad Guys. Instead, it is about the individual struggle of every person to make sense of their place in the infinite. Rather than simplistic "red lasers vs. blue lasers," a Planescape story is a story whose conflict is as internal as it is external, with the characters forced to make a choice between reasonable enemies and unreasonable allies, where the constant question is "What SHOULD happen here?" Because of element 1, this includes demons with a heart of gold and selfishness and angels who push too far. It is a conflict among the good and the thoughtful, a conflict where the "good ending" is far from clear. Because of this, it is a setting about what each character believes, what each character wants the world to be like after they've left it. It is a setting with infinite shades of grey, where your ideals matter more than what cosmic team you're wearing the jerseys of. Every angel is hiding a shadow, your demons are thoughtful, and your main antagonists are other mortal beings…and your own doubts.
3. You Shape Reality
While there are many games about small, local characters in small, local events that have major effects on individual lives, the most iconic Planescape games empower players to fundamentally alter the entire cosmos, according to their own vision. This fight might be long, and the struggle will certainly involve confronting those invested in another reality altogether, but the power to shake the heavens and twist the hells lies squarely with your characters. Your perspective has the possibility of becoming the objective truth, a reality defined by your own dreams and wishes. Of course, dreams can turn into nightmares, and some wishes are better off not being granted, so you will also need to face your own ideas run rampant, but when you emerge from this crucible, the very fabric of the multiverse will be forever changed by your hand. Your existence sends ripples through the world. That power — that responsibility — is yours to use as you can. It is also your enemies'.
What's all that mean?
…you know, in practice?
Take your most stereotypical excuse-plot fantasy D&D adventure: a wizard comes to a tavern and asks the party to retrieve a MacGuffin from a dungeon for various ambiguous wizarding purposes.
In Planescape, we need to take this to the edge. So it's not just a wizard, it is, say, a God of Wizards. One of the Exarchs of Ioun is coming into the tavern. The tavern, of course, is also an extreme tavern: perhaps it serves wine supposedly made from the apples of eternal youth. Distilled and diluted, it still causes those who drink here to look significantly younger for a few hours. Now, the MacGuffin isn't just some spell component — the God of Wizards needs this MacGuffin, so perhaps it is a long-lost spell once composed by a famous wizard like Bigby, and then lost to time…until Ioun's divinations learned of it. The dungeon isn't just a dungeon, it is perhaps the Shadow Cabinet of a Night Hag, a place where that loathesome creature keeps all of her trinkets from the soul trade, including this long-forgotten spell. It's not just for ambiguous wizarding purposes, Ioun seeks to have the greatest library in the multiverse and even now forces from Vecna and Wee Jas and Mystara are seeking the same spell, to add it to their collections and uncover its arcane secrets.
In Planescape, the conflict is not ultimately one of "beat the other guys," but rather a philosophical conflict of "whose ideas have the strength to prevail." So Ioun, Vecna, Wee Jas, and Mystara are all pursuing this spell, and they all are sending Exarchs to the various taverns of the world to search for adventurers to find their spell. The party is brought into the affair because their rivalry is causing chaos in the streets as magical battles spring up when the exarchs encounter each other. The party can side with any of these factions, or even pursue their own purpose for getting the spell — perhaps the party wizard would find it valuable for their spellbook, but perhaps the party thief would be excited to steal something from under the nose of a night hag, and the party fighter belongs to a faction that espouses sharking knowledge with others and would love to see it in EVERY wizard's hands, not squirreled away in some exclusive library somewhere. Not only can the party choose their patron (and thus their rewards), their choice is based on who they believe ought to have the spell, and what the spell means for all the patrons and each of the party members.
In Planescape, ultimately, the party members are those who shape the cosmos, so this little spell retrieval isn't just about a little change in some gods' power dynamics, either — it is ultimately about which idea the PC's want to prevail. Ownership of the spell isn't just about whose library it sits in — if Vecna gets ahold of it, the spell will be used as a weapon to increase the power of the forces of death. If Ioun gets it, worship of Ioun skyrockets and worship of this god of magic becomes nearly compulsory for wizards who want to advance. If our fighter gets it, perhaps he empowers a rebellious cabal of apprentices to overthrow the bonds of a church. These could all be good or bad things from certain perspectives, and it is up to PC's to choose a side they want to win, and to fight for it. What kind of world do they want to create? More than the gold reward, this is the reward they fight for.