This statement, from which the play derives its title, is ironic because the resolution of the murder depends entirely on those "trifles." For all their bluster, the men are mostly clueless as to the motive behind the murder, but the women figure it out almost immediately on discovering the dead canary. While looking through the kitchen, the men have the following exchange:
COUNTY ATTORNEY: I guess before we're through she may have something more serious than preserves to worry about.
HALE: Well, women are used to worrying over trifles. [The two women move a little closer together.]
(Glaspell, Trifles, etext.virginia.edu)
The women only discover the dead canary because they are looking for Minnie's patches for her quilt; without that motivation, "worrying over trifles," the canary would have been undiscovered. Even seeing the empty birdcage, the men only wonder where the bird went; if they had found the dead canary, they might have ignored its implications entirely. The "trifles" of the quilt and the empty birdcage, as well as the unkempt house, show the major reasons behind the murder, as well as to Minnie's emotional and mental state.