The show is set in a nearby, future Japan where nearly everyone has their own personal android. However, the androids aren't allowed to act independently or humanly, according to a certain definition of “human” that depends on an assumption that. However, in spite of that, they’re still capable of doing this, whenever hostile authorities aren’t observing this and through clever or self-interested interpretations of the "Three laws of Robotics"). That is, first, A robot may not injure a human being or, through inaction, allow a human being to come to harm. Second, a robot must obey the orders given it by human beings except where such orders would conflict with the First Law. And thirdly, A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.
The story is kicked off by our main character noticing a random note in his android's log that reads, "Are you enjoying the Time of Eve." Probing this detail out of curiosity, he notices that this data is tied to a certain location. When he decides to go there with a friend, they discover that “Time of Eve” is actually a cafe, where androids and humans could hang out without discrimination, or in most cases even the slightest indication that one is the other. While this is an initially disturbing concept for both of them, the cafe’s general mood and environment is rather tranquil, their host is welcoming and eager to serve, and the treats they sell are adequate. These things, but mainly the want of the main character to know more about this cafe and its patrons, entices them to stay a while and visit frequently. Since one of the few things to do in a cafe is talk, the main character and his friend mostly talk about figuring out who is human or android for themselves, without saying as much out loud. Meanwhile, each of these people(?) all seem to have their own story to tell about their lives.
Philosophy, making friends, lying a bit to spare feelings, or inadvertently hurting someones feelings, doesn't break any of the Three Laws of Robotics. Being in the Cafe, where "Robotics second law" is conflicted by the Cafe's own rule that no patron discriminate between android and human, isn't really breaking the "The Laws" either. This sort of talk is what overshadows much of the stories, and what accompanies the characters (and possibly the audience's) own question of "Who is the android or human?". After all, there are possibly valid questions to be had about the seeming absoluteness or rigidness of these Robotics Laws, and also ways to get around them once those questions reveal themselves.
The individual stories, which are told by the other characters, are more about the androids and humans grappling with their own wants and deeper needs, while dealing with each other, existing in the rather unfair world they were created or born in. The question of who's really a human or an android also gets quickly confused by the fact that, had it not been for the social fears of those outside about the supposed coldness and potential violence of the machines, the Androids would've likely lived like the humans around them do.
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tldr: Android shows independence because rules on how to live can be broadly interpreted. Two friends join a cafe where you can’t be racist to androids. They start feeling bad for their robot frens, because Bot Lives Matter.
Yes, I am enjoying the Time of Eve.