Aeri is the owner of Anga's Mill in The Pale. The Mill was passed down to her after her father died in the Great War against the Aldmeri Dominion. However her father also passed down a tax burden forcing Aeri to work even harder.
If asked, Aeri will give the Dragonborn Aeri's Note and request that it's delivered to the Jarl of Dawnstar.
If the Dragonborn has any Firewood Aeri will pay for each piece brought to her.
When the Dragonborn has completed any of the quest above Aeri becomes a candidate for marriage.
With the Hearthfire plugin Aeri will sell the Dragonborn Sawn Logs for the construction of their property.