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 the Overseer is purposely hiding information from the Vault dwellers.
The player 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 your advice and support, but nothing comes of it. There is no experience for giving advice and she never leaves the vault in-game.