One of the sillier things that Usagi ever did was name her daughter after herself, knowing that the poor kid would go into the past bearing her name. Everyone called her "Little Usagi," or "Chibi-Usagi," to distinguish her from the original Usagi; it eventually got shortened to Chibiusa. The poor girl didn't grow an inch past pink-haired kawaii little-girlness for almost a century, and didn't have any powers either. Her friends made fun of her for it. The only respect she got was from her parents and the senshi, who called her "Small Lady."
Let me backtrack. Chibiusa is the daughter of Usagi and Mamoru, born in the Silver Millenium of the future and raised as the young Princess Serenity. She grew to pink-haired little girlhood, and stayed that age for 900 years. When the Silver Millenium was attacked in the 30th century, Queen Serenity and King Endymion were defeated and Crystal Tokyo reduced to rubble. Poor little Chibiusa, having suffered the destruction of all she knew and loved, ran to the only friend she had left - Sailorpluto.
With the help of Sailorpluto, she travelled back in time, hoping to find the Illusion Silver Crystal of the past. With this crystal, she wanted to rescue her parents. (A bit illogical, I know, but she's just a scared little kid, bereft of home and family. She can't be expected to be logical. Besides, it worked.)
She literally dropped out of the sky onto Usagi and Mamoru, and latched herself firmly to the latter. Mamoru, for his part, was confused as to why he suddenly wanted to protect the little girl. (It made sense, seeing as she's his daughter and all. Mamoru-kun's subconscious, although wise, does not communicate with his conscious mind very well.) Usagi was just a bit jealous about the attention that Chibiusa was getting from Mamoru, despite the fact that Chibiusa was half her height and age. Chibiusa didn't do anything to make Usagi's life easier. She hypnotized the Tsukino family into taking her in, and shouldered her way into Usagi's life. She was scared, defiant, and piteously homesick by turns, and Usagi suffered through most of it. Also, the fact that she wouldn't tell anyone what she was looking for made her a bit of a mystery, and made the others wonder whether she was an enemy or not.
Chibiusa was born and raised a princess, and she tends to be just a little too aware of it. However, when all's said and done, she's still a child, and the total destruction of all she knew and loved shook her just a little bit. In fact, she blamed herself for most of the destruction. Wiseman was able to take advantage of her loneliness and vulnerability, and twisted her into the form of the Black Lady.
As the Black Lady, she was all-powerful, and nothing the senshi could do had any effect on her. She was able to fulfill the desires she'd had as a child, and summoned Mamoru to her side. Fortunately for all, Sailorpluto stopped time and killed herself in the process, and the death of her childhood friend snapped Chibiusa out of the form of the Black Lady.
After all that, Chibiusa joined the fight for justice as the senshi-in-training, Sailorchibimoon. She also became much more bearable, as she didn't have to worry about her home. Her attacks are very kawaii ("Pink Sugar Heart Attack!") and often done in tandem with either Sailormoon or Tuxedo Mask. As Sailorchibimoon, she helped save the life of Tomoe Hotaru, who became her closest friend. Eventually, she also helped save the unicorn Elios, guardian of golden Elysion, who was to become the love of her life. With this discovery, she realized that her crush on Mamoru was completely inappropriate (as well it was! The man's her father, for crying out loud), and resigned herself to growing up.