"Aunt Jennifer's Tigers"
From the title we can assume that the speaker have an aunt name Jennifer.
Aunt Jennifer's tigers prance across a screen,
The speaker could be describing a tiger on a wall décor or on a flat surface.
Bright topaz denizens of a world of green. A topaz is a shiny crystal, and denizen means an inhabitant. So the speaker was trying to describe the tigers as bright, crystalline animals that prance around their forest.
They do not fear the men beneath the tree;
The speaker is telling us more about the courage of the tigers. The tigers do not fear anything or maybe not even human.
They pace in sleek chivalric certainty.
The tigers are brave, courteous, and loyal and the pace with a certain style that make them sleek.
Aunt Jennifer's finger fluttering through her wool
Now the speaker is finally come back to Aunt Jennifer and giving us a picture of her. Aunt Jennifer finger is nervously swifting through the tiger’s soft fur.
Find even the ivory needle hard to pull.
Looks like Aunt Jennifer is sewing some type of quilt and looks like she’s having a hard time to pull the needle.
The massive weight of Uncle's wedding band sits heavily upon Aunt Jennifer's hand.
Sound like Aunt Jennifer is having some difficulty on her marriage with “Uncle” and it is taking a toll on her and even on crafting, needlework maybe the simple thing that a woman enjoyed.
When Aunt is dead, her terrified hands will lie
still