Judging from the extended featurettes we've seen so far, the pilot for NBC's Constantine focuses on John Constantine's meeting with the ordinary woman Liv, who gets caught up in demonic business and needs to team up with Constantine to survive. But don't get too attached to Liv.
According to The Hollywood Reporter, the character of Liv has been written out of the show, and actor Lucy Griffiths (True Blood) has been let go. They're not recasting the character, just getting rid of the show's female lead. Instead, one of the first few episodes of the series will introduce the character of Zed, who becomes Constantine's "right-hand woman" in the comics. Zed hasn't been cast yet. The show will also be introducing a number of other comics characters over the first half of the season.
Liv was described as "an offbeat woman who finds herself teamed with Constantine after she is marked for death by a powerful demon. With the ability to see the supernatural world among us, she becomes a key player in the battle between good and evil." It doesn't sound as though they're reshooting the pilot to get rid of her — she'll still have a major role in the pilot, but then she'll be written out soon afterwards, reading between the lines.
And that's probably a good thing. Not every supernatural show needs an ordinary human to serve as the "audience-identification character" who discovers the supernatural world as we do. This show might actually be more fun without her.
Here's a clip from the pilot, featuring Griffiths: