I like her because she is cool and because of her powers.

Orihime's power manifests itself as the Shun Shun Rikka ( literally "six flowers of the shielded hibiscus", translated in the English anime as "six princess-shielding flowers"), six fairy-like creatures that reside in her hair-clips (shaped like six-petaled flowers, each fairy is two points on a given clip) when inactive.
The fairies are separate manifestations of Orihime's spirit, each with its own unique appearance and personality, and each named after a flower. Orihime's techniques involve incantations manipulating the Shun Shun Rikka into three different groups. Though Orihime initially needed to chant an incantation to use her techniques, further training has rendered this unnecessary. Her incantation consists of voicing the names of the members involved, followed by the technique name and the phrase "I reject" (watashi wa kyozetsu suru?), a reference to the nature of her powers.
Santen Kesshun (literally "triple heavenly linking shield") is Orihime's defensive technique. The incantation arranges Baigon, Hinagiku and Lily into a triangle, forming a barrier capable of repelling anything seen so far.
Koten Zanshun (literally "solitary heavenly cutting shield") is Orihime's offensive technique. The incantation summons Tsubaki who forms a thin barrier on either side of himself that cuts through enemies like a sword. However, when Tsubaki is destroyed by an arrancar, Orihime is unable to use this technique until Tsubaki is revived.
Sōten Kisshun (literally "twin heavenly returning shield") is Orihime's healing technique, though it goes well beyond simple healing. The incantation summons Shun'ou and Ayame to form a half-oval barrier around whatever or whomever Orihime wishes. While active, the barrier repels all negative events inflicted upon anything within the barrier. No matter how extensive the damage may be (whether used on living beings or inanimate objects), the barrier can restore it to full working order by reversing space and time around the damaged area, making it as if the object was never damaged in the first place. This is the aspect of her power that piques Sōsuke Aizen's interest in her since, in Aizen's words, she "violates the realm of gods."