I don't get it. This was a surprise mega-hit in Japan, but I can't work out why. It's nice. (Admittedly the full backstory is going in extremely not-nice directions, but I'd say the show's fluffy niceness manages to trump even that.) It's got lovable animal girls exploring "Japari Park" and befriending each other. There's nothing wrong with that and I enjoyed the show, but I'd have never guessed that it went super-ballistic domestically and I'd advise putting that peculiar fact from your mind should you ever get around to watching this.
I expect you'll like it. However this isn't the kind of show that's improved by high expectations. It's gentle, cute and a bit on the forgettable side, to be honest. Oh, and it also has super-cheap CGI animation, but you won't care about that because the characters are all charming and it's being carried by the voice actors.
The setting is Japari Park, which is presumably short for "Japan Safari Park". All the characters but one are Friends, which is their term for animal girls created by something called Sandstar. If this substance touches an animal (even a dead one), then a Friend might be born. These Friends will be female and basically human, but they'll have no idea what they really are (e.g. not knowing that they're wearing clothes and that those can be removed) and they'll have characteristics based on the animals with which they still identify. Chameleon has a magical cloaking ability far more powerful than a real chameleon's colour-changing, for instance. Serval can jump and lift like Spider-Man. (She's incredible.) A bird-based Friend will be able to fly, seemingly by flapping her ears. There are even Friends based on legendary and/or semi-mythical animals like the Tsuchinoko.
The exception to all that is Kaban-chan. Serval calls her Kaban (Japanese for "bag") because she carries a bag. Serval's a simple cat. Kaban-chan's a bit of a mystery, being a hitherto unknown animal that has hands, uses tools and is good at thinking. No one has any idea what Kaban-chan might be, so she sets off with Serval to explore Japari Park in search of other Kaban-chans who might know more information.
The coolest thing about the show, for me, is its zoological angle. Every episode will have its own guest stars and a brief educational voice-over from zookeepers about a couple of real-life animals' quirks and habits. This can be nifty. I like owls even more now. The Friends will reproduce odd little characteristics you hadn't known about, while the show's animal choices are never predictable. Sometimes they'll be famous (lions, hippos, giraffes) and sometimes I'd never have heard of them (campo flicker, fossa, margay, gentoo penguin).
As for the episodes, they're gentle mini-adventures as Serval and Kaban-chan explore different park environments and help Friends with their problems. This isn't hard, since Friends don't usually have much common sense and will be astonished as Kaban-chan demonstrates human-level intelligence. The good news, though, is that this is characterisation rather than the show laughing at idiots. (Fire scares almost everyone, for instance.) There's a lot to think about in this world, e.g. the Friends' long-term prospects since they're always female. (That's true even when they came from male animals, so for instance the Lion Friend has a mane.) There are plenty of indications that the truth is darker than the fluffy adventures we're watching, starting with the Friend-eating alien Ceruleans that only look cute and harmless. I won't spoil the backstory that we eventually learn, but that takes those deeper implications to yet another level.
I'm not going to try to psychoanalyse the domestic viewing audience, but I don't mind the show's success. It's a likable anime that anyone could watch. Technically it's based on a mobile game, but one that had performed badly enough to be discontinued a month before the anime's debut. No one had thus expected a sleeper hit like this... but the most surprising part is what the copyright owners (Kadokawa) did next. The anime's director, Tatsuki, had basically conjured up a hit out of nothing. He created the characters seen in this show, which is technically a next-generation sequel to the original game rather than part of it. He even animated a bonus mini-episode 12.1 for free and posted it online. Kadokawa responded by firing him for copyright violation, then forcing a public apology from the voice actresses (who'd had nothing to do with it) when the Japanese fanbase erupted in rage. The company's stock dropped over 3.3% in a day because of this and the anime's entire staff resigned in protest. There will be a second season, but it'll have an all-new production team and the fans already have their knives out for it.
I'm not convinced that it'll be that different, though, because frankly I don't think Season 1 was that special. It's charming and even interesting, but this isn't a show to blow you away. It looks and feels like a kiddie show, e.g. the endearingly rubbish animation. (It's darker underneath, though, and the characterisation and worldbuilding is clearly superior to what you'd assume if you walked past the TV while it was on.) Watch it, but don't get misled by all the talk about it.