Fate/Apocrypha diverges from the core timeline wayback at the Third Grail War, which is now established as having been during the Second World War. During that war, the Yggdmillennia family straight up stole the Greater Grail and proceeded to hang on to it. Since then there have been a series of smaller Grail Wars, until finally we have a Greater Grail war, between the forces of Yggdmillennia (the Black faction) and the Mage's Association (the Red faction - no relation to the game series)), to see who will control the Grail. Arbitrating this is a Ruler - a Servant sent to make sure the rules are followed - in this case Jeanne D'Arc.
However, to quote the Lord of the Rings... they were all of them deceived.
During that 3rd Holy Grail War, that war's ruler - Amakusa Shirou Tokisada (yes, Samurai Shodown fans - that Amakusa) - managed to stick around after the war with a cunning plan - get into the holy grail war, and make a wish on the Greater Grail to cause - in short, Third Impact, to stop human suffering, like what happened to his followers in the past.
So that shoe gets dropped about midway through the show, and that absolutely changes the dynamic of the series - with the remaining master of Red and the surviving masters of Black basically responding to that revelation with "Well, f*** that!" and banding together to stop it. Well, that and trying to stop Assassin of Black (who is Jack the Ripper) from running amuck.
This leads to the second half of the series being having both heavier characterization, fights with higher stakes, and more impressive animation for those fights. We get Gordes coming to view the Homunculi as human, Sieg understanding how he feels about life and humanity, and Jeanne's growing affection for Sieg.
We also get some of the most impressively animated fights of the series - Achilles and Chiron, Sieg(fried) and Karna, Jeanne (and later Achilles) and Atalantia. It's gorgeously done work - though I will admit going from comments elsewhere that some of the animation in those fights is more divisive than others.
All of that said, while the fights are impressive, and some of the character beats in the second half of the show are nicely done, it's a little inferior to Fate/Zero - mainly due to some issues with the material. If you're already deep into the Nasuverse lore, there's a lot to enjoy - but if you're new, there is other material to go with.
