Elektra Natchios is a character created by Frank Miller for Marvel Comics. Her character first appeared in Daredevil #168.
Based loosely on the Greek Agamemnon myth, Elektra's story goes something like this:
Elektra's mother had an affair, so her husband (a Greek diplomat) looked the other way while his son (Orestez) plotted his mother's murder.
Shortly, Elektra's mother - pregnant with Elektra - is indeed murdered, but Elektra is saved.
Elektra grows up sheltered by her father. She is physically gifted, and becomes quite accomplished in the martial arts. Eventually she seeks out an elite order of monks (the Chaste) to continue her training. The Chaste initally accept her entry into their ranks, but the dark feelings inside Elektra eventually force her expulsion.
Round about this time, Elektra travels to the U.S. and enrolls in Columbia University. There she meets and falls in love with Matthew Murdock, a.k.a. Daredevil.
Unfortunately, this happy period of her life is cut short when her father is murdered. Elektra, shattered, leaves abruptly and joins the dark cult of the Hand.
The naive Elektra plans to prove her worth to the Chaste by subverting the Hand from the inside, but instead she only strengthens the dark side of her nature.
Eventually, Elektra does break rank and escapes the clutches of the Hand only to become a mercenary assassin. During this period, she encounters her old flame Daredevil - but not as a friend or lover - as a foe.
Elektra and Daredevil spar several times before Elektra is killed by a rival assassin, Bullseye. But even in death, Elektra cannot escape her past. The Hand exhumes her corpse in order to resurrect her body and use it as a weapon against the Chaste.
Fortunately, Daredevil and the Chaste learn of this plot and foil it. Elektra is not revived, but her soul is cleansed through the efforts of her past love, Daredevil.
Thus ends the Elektra saga...well, not really. Apparently, in her new purified state, she is revived by the Chaste, and lives. Now she is a force for good (but in my opinion, a much less interesting character).