She asks the Dragonborn to be her father/mother, even if her parents are alive.
Giving her 1 grants the Gift of Charity blessing (+10 Speech for 1 hour real time).
Svari is amazed that dragons are real when she is told that the Dragonborn is a Helgen survivor. She then says she needs to remember to tell "papa" that they are real.
Apparently if you run a mod that allows children to die and are in good standing with Svari, the Dragonborn will get a Letter of Inheritance and the sum of 100 gold, 10 of which is taxed by the jarl's court. Since children cannot die normally, it's assumed that the game is set up so that anyone who dies that trusts the Dragonborn will give the Letter of Inheritance.
If you kill Svari's mother she will hire thugs to kill you, though the contract may have a mistake, as Svari misspells her name as 'Savari.'
If the HearthfireDLC installed, she will be sent to Honorhall Orphanage if her parents both die. It is then possible to adopt her.