Liza is a witch who’s buried just outside of the graveyard in “unconsecrated ground,” otherwise known as the Potter’s Field. As Silas explains to Bod, the main graveyard is built on land blessed, or consecrated, by a church. As Liza explains to Bod, she was accused of being a witch, and then burned to death, some 500 years before. The twist is, Liza really was a witch, or so she claims.
She doesn’t ever tell Bod what that means, or what kind of witch-y activities she performed, other than causing everybody who watched her burn to get the plague and die. If she was anything in life like she is as a ghost, it’s not likely she used her witch powers to hurt people on a day-to-day basis. From her actions with Bod, she seems to be a helpful, goodhearted person.
From the time Liza and Bod meet, Liza assists Bod in each of his major adventures. She helps him escape from Abanazer Bolger, the crooked pawnbroker; she alerts Silas when he gets arrested; and she helps him when he’s battling the Jacks. Their friendship is cemented when Bod risked everything to get her a proper headstone.
As readers understand, but Bod doesn’t, Liza has a serious crush on Bod.
When she knows, but Bod doesn’t, that Bod is about to leave the graveyard, she tells him he’s “too foolish to live” (8.34). When she plants a kiss on him afterwards, her love for him becomes clearer, at least to readers, and we can get what she’s saying. She’s basically trying to say that she wishes Bod would die so he could be with her – she doesn’t quite mean this literally. She wants only the best for Bod. This is just her version of being romantic.
Liza’s crush on Bod doesn’t start until Bod becomes a teen. We don’t know how old Liza was when she died, but we know from Bod’s description that she was a teen. In Bod, Liza sees the opportunity to get what she missed out on in life.
Still, she knows it’s impossible. This is probably a big part of why she stops speaking to Bod after a while. She knows that hanging out with him will only make her like him even more. But even when she isn't talking to Bod, she never lets him down when she thinks he might really need her. That tells us that her love for him is pure and unselfish. And that makes us feel even sadder for her. She just keeps getting the short straw!
In his Newbery Acceptance speech, Neil Gaiman reveals that Chapter 4, the chapter that introduces Liza, was the first chapter he wrote. Liza’s inspired by a grave in the graveyard Gaiman played in as a child in Sussex, England. As a kid, Gaiman thought witches were buried in that grave. As a teen, he learned that the three women that shared the grave were actually Protestant martyrs who were burned by order of a Catholic Queen (source). (To make a very long story short, Protestantism is a Christian religion started by people who wanted to reform the Catholic Church. A Protestant martyr is someone who refused to give up his or her Protestant beliefs, even under pressure from the Catholic Church.)
In the US, most of us hear about witch burnings with the Salem Witch Trials. Witch-hunts also happened in other countries, including England. Part of what The Graveyard Book does is try to show us another side of beings that have a reputation for being scary and evil (mummies, werewolves, vampires, ghosts, and witches, for instance). With Liza, it’s a little different. Since she’s based on women who weren’t really witches, it’s possible that Liza wasn’t really a witch either, but was just having fun acting like one for Bod (you have to entertain yourself somehow after being dead for 500 years). Her revenge story might just be wishful thinking. On the other hand, anything is possible in The Graveyard Book.