She is the leader of the rebel faction in Vault 13 after the Vault Dweller comes back with the water chip. The rebels are concerned about the health of the members in the Vault and think that OverseerJacoren is purposely hiding information from the dwellers.
The Vault Dweller can also offer her advice by telling her about Shady Sands and suggesting that it would be a good place to go first once they were out of the vault. Theresa would be grateful for the advice and support, but nothing comes of it. There is no experience for giving advice and she never leaves the vault in-game.
At 1700 hrs every day, the rebel faction convenes in her room. If the player character fails to convince them in the meeting, Theresa warns them not to get in their way. If the Vault Dweller says they can not let them do it, the rebels will turn hostile.