I have seen the Anime and I own all the Manga so I'll tell you. The show is more for older kids (The Manga is rated 16+)
Im basing this on the Manga, the Anime shows more stuff that isnt in the Manga. CONTAINS SPOILERS
So its about this dude named Hideki Motosuwa, he goes to Tokyo for Cram school. He finds out about these robots called "Persocoms" (AKA, A Human Designed Robot) He can't afford one but he wants' one. One day after coming home from his job, he finds a Robot in the trash. He turns her on (Dont ask how o.o'') And she can only say "Chii" So Hideki names' her Chii. He thinks Chii is a broken robot, but when he finds out she may be a "Chobit" from his friend Minoru, the trouble begins. Chii has another "her" (Her sister, before Chii was thrown away. And Freya *sister* died, leaving her program in Chii) And Freya is helping Chii find Chii's "Special Someone" Along with some help from a book by Chii's former Owner. Since Chii has a special gift to hack into other Persocoms against their owners will, the government is after her. Along with another dude.
Thats as small as I can summarize it. I can put WAAAAAY more. Ill show you a picture of my Manga collection