Divine Beast Cave Back Floor
This is your first dungeon and the first Back Floor you'll come across so much like the old guy did, let me give you a more advanced run down. To enter each back floor of a dungeon you must obtain an item and bring it to the "?" on the map. Doing this will grant you access to the back floor.
Back Floors have much better loot than normal floors and all the mobs in the back floor have the stamina buff, making them hit twice as hard. I highly recommend you use Xiao for almost all the back floors once you get her as she can avoid almost all the damage and kill just about every monster in the game with ease.
Also, probably the most important part of venturing into the back floors is just about every one of them gives you a gem which is a pretty useful component when it comes to weapon customization. Also, another good bit of information is once you unlock the back floor on that floor as long as you don't leave the dungeon you can keep going back to it and killing the monsters. The treasure chests will still be opened however; the only use for returning to an already cleared back floor is to level up your weapons.
To reach the first dungeons back floor keep an eye out for an item called "Tram Oil" this you can use at the tram and ride it to the back floor of the first dungeon. A picture of Tram Oil is below