Hi there!
Brains: Mental acuity. Use Brains to outsmart a threat, focus on ingenuity to overcome an obstacle, or use your knowledge to seek clues about something.
Brawn: Physical might. Use Brawn to climb a cliff, move a heavy barrier, or hold on tight as your dragon is flying through a storm.
Grace: Nimbleness (usually physical, but not always). Use Grace to hop across ice floes without falling in, quickly weave through dense underbrush, or bow and flatter your way across the royal ball without anyone realizing there's a dragon tucked into your tunic.
Heart: Determination and emotional resilience. Use Heart to resist a wizard's fear-based magic, talk down a bounty hunter, or convince an angry adult dragon that you and your baby dragon are not a threat to their territory.
This is how I think about these attributes, but they are open to some interpretation. In the game, the attributes are described only by their names for two reasons. First, it saves space so the game more easily fits on a single page. Second, which attribute to use is mainly about a player's description and a discussion of what's happening. There are lots of gameplay cases where an uncertain moment could use any of two or three different attributes; talk about it and agree on one. It's fine if a Keeper tends to assert attributes they're better at; they all incur the cost of wearing down those die sizes and increasing the pressure to rest.
Rope and 'Exploring': Exploring is traveling through unfamiliar locations. (A group can flex that definition, if they want.) Not all exploring will need a check -- walking along a road or trail is not dangerous enough or dramatic enough to consult the dice -- but when exploration gets dangerous or dramatic, you'll probably want to ask for a check or two. In cases like this, were there's a check in service of traveling unfamiliar locations, a Keeper takes +1 if they rely on their rope for that check.
For example, let's say a Keeper is walking along a narrow ridge in strong winds. If they want to use their rope to tie themselves to an anchor point, they can roll with their rope's die instead of an Attribute; and, since they're rolling in service of traversing the environment, they get the +1 bonus. If a Keeper is using rope for some other purpose, such as tangling a monster's legs to escape it, they can still roll the rope's die, but since this isn't exploring they don't get the +1 bonus.