Plot:
The story begins with a young girl named Lucy escaping under odd circumstances from an insular researchfacility off the coast of Kamakura in the Kanagawa Prefecture of Japan. Lucy manages to nonchalantly dismember and slay a fair number of the staff and guards with a form of seemingly super natural power and gets outside. A sniper is seen trying to shoot her, only managing to ricochet a bullet off her
metal helmet. Lucy then falls off a cliff into the sea, bleeding from
her head but ultimately surviving and evading the research staff.
Lucy is not a normal human but rather a diclonius: a mutantvariant of humans with two small horns on their heads (hence the name diclonius) that resemble cat ears. The diclonius race possesses telekinetic powers through use of their "vectors", long arms that resonate at a
speed that causes them to be undetectable by sight. The number and
reach of the vectors depend on the diclonius. All diclonius seem to be
girls only. There is not one mention of a male diclonius throughout the
whole series. They also all have pink eyes and hair unlike regular
humans who have brown, black, blonde, and red hair.
The day after Lucy's escape, a boy named Kohta arrives at Kamakura to meet his cousin Yuka. Kohta has come to study at the local university and has been given lodging at an old, family-owned inn, the "Maple (Kaede) Inn", provided he acts as the caretaker.
After meeting with Yuka, they go for a visit to the beach and find Lucy
washed up on the shore, still naked and bleeding from her head. The
head trauma Lucy experienced causes her to develop a split personality.
In stark contrast to the cold and sadistic Lucy, this personality is
completely docile, harmless and is incapable at first of saying
anything other than "Nyu". Not knowing what to do with her, Kohta and
Yuka take her back to the inn to look after her and name her "Nyu".
Yuka quickly decides that it will be best that she also live at the inn.
Kohta, Nyu, and Yuka begin settling into their life at the inn and
Nyu begins to dredge up painful repressed memories from Kohta's past.
Meanwhile, the researchers from the laboratory where Lucy was held
begin searching for her, dispatching both human and diclonius agents to
hunt her down.
Main Characters:
is a teenage diclonius girl around 18 years old, Lucy has four vectors with a limited range of two meters. However, she can be swift and lethal within that range, and will use any nearby objects as high velocity projectiles
to kill at greater distances. She is also capable of stopping or
deflecting most standard ammunition when she concentrates on the task.
Lucy hates humans mainly because of how she was treated by her human
peers as a child. Consequently, she discounts non-diclonii, claiming
they are not real people. She seems to lack empathy,
kills without much concern, and acts somewhat sadistically. Despite
this lack of concern for human life she will not harm Kohta.

is a split personality of Lucy that developed after a .50BMG round ricocheted off a metallic helmet encasing her head. Nyu has a
childlike personality and infantile knowledge of the world, forgetting
even that she is a diclonius and how to use or manifest her vectors leaving her a human with horns. She initially lacks spoken language skills; however, she eventually learns a handful of words and phrases. Nyu is innocent and incapable of violent acts, a foil
to the normally cold and sadistic Lucy; she is the manifestation of her
"good side". When Nyu is attacked violently (or hit on the head), she
regresses into Lucy; likewise, when Lucy is treated with love and
kindness, she will uncontrollably switch back into Nyu.

Kouta (コウタ,
Kōta)
is around 19 years old and enters the story when his cousin's family
allows him to move in to their closed down inn in exchange for
maintenance while he goes to a local university Kouta has repressed traumatic memories
of his father's and sister's deaths during his childhood at Lucy's
hands. Because of his repressing his memories, Kouta does not remember
Lucy from when he met her earlier as a child. Due in part to his loss,
he has a soft spot for girls in trouble and is extremely generous and
protective to the girls around him. He is more forgiving in the anime,
but in the manga when he gets his memories back he truly is unforgiving
about Lucy killing his father and sister.

Yuka (ユカ, Yuka)
is Kohta's cousin. She is also around 19 years old and planning to attend the same university as Kohta. She moves in with him at the inn after having not seen him in many years. Having had a crush on Kohta since childhood, she is in love with him, and is therefore jealous of Kohta's attention to Nyu, to the point of being very irrational.
(info. from wikipedia.com)
what can I say???
Well... I just noticed one thing...

Don't
Nyu and
Orihime look almost the same??? xD