Katrina is the town greeter standing at the front entrance to Shady Sands. The likely intention of the developers of Fallout was to include her as a tutorial character, considering her dialogue is focused around explaining a few fundamental game-play systems, including bartering, healing, and the First Aid and Doctor skills.
This quest is very straightforward; exhausting all possible dialogue options with Katrina will yield an experience reward. Note that she will not talk to a character armed with any weapon, as she encourages peace and diplomacy in the small community.
A Vault Dweller with a low Intelligence will not be able complete this quest as Katrina will not hold a conversation with a dumb character, simply stating that he is not competent enough to communicate. This ends her dialogue, and leaves the quest incomplete.