How Does The Mordant, Ferric Acetate, Interact With Tannins When Ebonizing Wood?
A mordant is a substance used to set dyes on fabrics or tissue
  sections by forming a coordination complex with the dye which then
  attaches to the fabric or tissue (source).


Tannin is a biomolecule consisting of many carbohydrate and polyphenol residues with plenty of hydroxyl and carboxyl groups. Tannic acid is a common type of tannin:

$\ce{Fe^{2+}}$ and $\ce{Fe^{3+}}$ form colored complexes with these oxygen-containing functional groups. These iron-tannin complexes change the color of the wood. The color intensity increases with tannin content of the wood and can be increased by the addition of tannin-rich tea. Structures with a varying coordination sphere of iron are formed, some of which are shown here (sources: 1 and 2):