Here's the only thing you need to know about Robbie: he loves Gloria. Oh, and he's a robot. So those are the two things you need to know about Robbie, and those two things are definitely related. As Gloria's dad notes, "He just can't help being faithful and loving and kind. He's a machine—made so" (76). Robbie is the robotic nursemaid and companion of Gloria Weston.
That's kind of a funny notion, the idea that a robot could be programmed to be the perfect companion for a kid; but he definitely seems to be a great companion to Gloria. Notice how much fun they have together at the beginning of the story. (Notice also how much Asimov describes the scene; it's like he really wants us to be able to imagine a child and a robot playing together.) And since this is our first introduction to robots in this book, Robbie kind of sets the stage for how we should think about robots in this book.
That is, in some ways, Robbie is a simple, clunky robot—he was built in 1996 (Introduction.39); he can't even talk; he's described purely in geometric terms (like, his head is a parallelepiped (15)). So he's a typical robot. If this were a movie from the 1940s, he'd be played by a guy wearing a cardboard box painted silver.
But in other ways, Robbie is a complex and emotional creature; for instance, he loves stories (25), which isn't what you usually expect when you think "robot." And, more importantly, he loves Gloria. So by starting I, Robot with this story, Asimov lets us know that the robots here are going to be different than what we're used to: they are going to be more human.
What does this robot tell us about robots? That they can be emotional and more human than the robots we might be used to from other works of science fiction.