Monster Hunter is hard to describe, but imagine it as "Boss Fights: The Game". People find a lot of parallels with Dark Souls - very deliberate combat with attacks that leave you open to being wrecked if you aren't careful. Unlike Dark Souls however, there's no leveling, only getting good will solve your problems. Most hunts have a limit of 50 or 30 minutes, and it's not unusual for the harder monsters to have your initial kill take that long. It has an absolutely huge following in Japan, but it really didn't explode in the West until Monster Hunter World came out.
The game cycle consists of hunting monsters, carve up the monsters into parts, turn the parts into weapons and armor, use the weapons and armor to hunter bigger and meaner monsters. Occasionally you change 'tiers' or 'ranks', however that particular game refers to it. Stuff will hit harder, have more attacks, newer even more aggressive monsters will be added.
The playstyle variety comes from which of the 14 different weapons you main. As an example, The great sword is a giant slab of metal that encourages a hit and run style gameplay. Line up one massive hit, connect with the mob, and get away so you can set up the next hit. Compare this to the dual blades, where you become a blender of many smaller hits, Naruto running around the monster and hacking at their ankles nonstop.
Honestly, it's one of my absolutely favorite game series and I can't wait for the new one to come out next week. I've put hundreds of hours into multiple titles, and it continues to be one of the most rewarding and satisfying game series I've ever played. I think it would be an amazing collab game, and I eagerly wait with bated breath to see if anyone picks it up as a regular game.