Houseki no Kuni is certainly an odd canon. There's a lot of setting info to take in, between the character's odd species to the dystopian world in which they live. I'll try to break this down piece by piece but be warned -- it's a wild ride.
The premise of Houseki no Kuni is simple on its face (or at least it starts out that way), while the actual mechanics are a little complex. The setting takes place in a future where humanity has already gone extinct. Six meteor strikes hit Earth, wiping out the population and a majority of all animal species. All that's left is the vast ocean and a small strip of land.
The main characters in this series are semi-anthropomorphic gems. Made entirely of the rock from which they're named, these gems are sentient beings with a humanoid appearance. According to canon lore, the gems rose from pockets of humans who fled to the sea, only to crystalize and re-emerge on land.
There are a lot of "rules" to the gem species -- while they look 80% human, they are certainly a unique species that don't function at all like we do:
Of course, gems are made almost entirely of a specific type of gemstone. Based on a gem's name, ie Diamond, you can tell what material they're made from.
Gems obviously function very differently as compared to human anatomy. First of all, they have no internal organs. Of course some of their bodily functions don't make sense, like thier ability to speak or blush, but they don't have a need to eat and don't bleed. They're massive, moving rocks, essentially. They don't have a brain -- it's more like their whole body is their brain. They hold memories within 'inclusions' that keep their bodies together and functioning.
Similarly, the gems don't breathe. This only truly matters in that they can talk underwater and in other circumstances that typical humans couldn't.
Since they are, again, giant sentient rocks, the gems are immortal in the most absolute sense of the word. If a gem shatters, it can typically be put back together again. If not, its pieces can be kept in order to try and find suitable fragments to attach it to, bringing it back to life. Gems shatter frequently, though most can be easily repaired. They don't feel pain and can lose major extremities with little to no effect. A gem's head can be cut clean off and reattached, only losing memories proportional to the shards that couldn't be recovered. Gems also can't really touch each other. There are exceptions to the rule, but because they vary in hardness, a gem can touch another gem and shatter or chip them. Thus, gems only really touch each other when they're wearing gloves or other protective clothing.
You might notice that gems are #ffffff, WonderBread White. Why is that if they're large gems? In canon, gems use a special powder that protects them from the elements. The powder is hardy and sticks to them, usually for a long time or until it's scraped off and their actual colour is revealed. You can tell what colour a gem is usually by their hair and/or their eyes. Why do gems have hair? No clue -- but if a gem loses some shards, their hair is cut and the pieces are used to repair them.
While gems don't need to eat (they usually get any energy they need from the sun), they do need to sleep. While losing sleep isn't detrimental for a gem, most of them hibernate during their world's winter. It's not like a bear hoarding food and crawling into a cave -- they essentially have a pajama party and pass out for months.
Finally, all the gems are inherently sexless. They have no sexual organs and are androgynous in appearance for the most part. Gems are also genderless, though most of them default to male pronouns. In canon, the gendered words used between the gems can switch (also based on translation), and the canon's updated Wikipedia refers to all gems by "they" -- this is perhaps the most accurate pronoun for the gems, but again, most gems refer to themselves with male-gendered Japanese terms. For instance, older gems are often referred to as older brothers.
Gems aren't the only species found in Houseki no Kuni, though. The main conflict of the series is that the gems have to protect themselves and their land from Lunarians (tsukijin) -- a species of spirit-like creatures that come to Earth from the moon, hoping to capture gem shards to take home. The gems must fight them in order to keep themselves and their gem siblings safe, and sometimes it's possible that gems that have been abducted can be recovered via shards the Lunarians carry. Another species is Admirabilis, jellyfish-like creatures that live in the ocean and do have sex and gender constructs.
While most animals have died out, there are some living things that can be found on land. There is grass and some foliage, snails and some insects, berries and flowers, herbs and shrubs. The land that is present goes through seasons and has a variety of topography, from a swamp to a forest area. There are multiple beaches with crags and caves -- gems may not be able to recognize an animal like a cat or a dog, but they do have a very basic yet varied ecosystem.
When it comes to technology, the gems aren't all that advanced. Instead of electricity, they use jellyfish as lighting. They are self-sufficient, making their own "medical" supplies, textiles, clothing and other items like weapons.
Finally, gems do have a pretty intimate culture despite being immortal. While there is of course a melancholy that happens when a gem is "destroyed" or abducted, grief certainly isn't the word for it (though you could say Phos does experience grief and guilt when he's responsible for a gem abduction). The gems typically see each other as family, "brothers," that should look out for each other. There's not a lot of open dislike -- they squabble and bicker like childish siblings, but they do care for each other. They also revere their senior gem, Adamant-sensei, for the most part.