Since arriving on the island, Kate has been involved with most of the major developments that occur to the survivors, from the recovery of the transceiver, to the discovery of the repeating transmission, the polar bear, the cave-in, and the decision to move to the caves. This is due in no small part to her friendship with Sayid, Charlie, and Hurley, as well as her apparent feelings for both Jack and Sawyer.
In "Walkabout," Kate refuses to help Locke kill the boars, even though her father trained her how to hunt, and says, "I'm a vegetarian." In a later episode, however, she is seen killing a shellfish with Sawyer helping her get the food for others on the Island.
During a game of "I Never" in "Outlaws," Kate reveals to Sawyer that she was married, though she says the marriage didn't last very long (her marriage to Kevin). She also reveals that she has killed a man, although she may have been referring to Tom, as she also tells Jack that the toy airplane "belonged to the man I killed."
Later, Kate helps deliver Claire's baby boy in the middle of the jungle, while Jack is in the midst of trying to save Boone's life.
When Sawyer dumps out the contents of her backpack, he finds out that she is carrying the passport of a survivor who drowned a few days after the crash, presumably to use for future false identification, in "Born to Run." He then tells everyone about it because she made a statement that she would take his spot on the raft.
Text Credit: Wikipedia.org