HR is Hunter Rank. Hunter Rank is like your "level". There are so called "key quests" that unlocks "urgent quests" and when you complete a urgent quest, your HR will go up, meaning that you can hunt bigger and harder monsters. When you do that, you get better equipments. HR 0-2 are low rank, 3-5 high rank and 6+ are G-rank. Dunno if there's something more, I just got HR6 myself. You really doesn't know what's the key quest if you don't use any guide. And trust me, you will end use guides A LOT. And that OK, since that's what thats about. There isn't tutorials that will hold your hand and grand instant kill Deviljho if you wet yourself when it arrives, but there is MH community! Other players are kind and helpful, so no elitist bastards here like in other games *coughwowcodloletccough*
Here's couple of helpful links:
Weapon trees: http://www.gamefaqs.com/3ds/642342-monster-hunter-3-ultimate/faqs
Ultimate Hunter Helper: http://monsterhunter.wikia.com/wiki/Monster_Hunter_Wiki
Monster Hunter Wikia will include all info that you will need when you hunt. Key quests, monster data (weaknesses and stuff), skill info, weapon and armor set infos and etc. I have it always open in my tablet or cellphone when I'm playing.
Hopefully that helps.
PS: 78h and FINALLY HR6! G-rank quest farming ahoy!
