It is clear in this excellent play that the person who killed John Wright was actually Minnie Wright, his long suffering wife who had changed so much through her marriage to her husband and the cold, stern disposition that he had. Of course, the intense irony of the play is that the men are self-importantly wandering around trying to find a motive to incriminate Minnie Wright, but it is the women, who are mercilessly mocked and patronised for their focusing on "trifles" that actually find the missing clue that allows them to piece together a motive that indicates it was Minnie Wright that killed her husband.
They find a dead, strangled canary, that obviously belonged to Minnie Wright. Of course, John Wright himself was strangled, and note what Mrs Hale says to Mrs Wright regarding it:
If there'd been years and years of nothing, then a bird to sing to you, it would be awful--still after the bird was still.
This helps us to see that having experienced mental, psychological and physical overshadowing from her husband, and then having her canary strangled in front of her eyes, Minnie Wright would have lashed out in a fit of desperation, strangling her husband in his sleep. The women ironically solve the crime that the men are unable to do, but they choose to hide the missing bit of evidence from them in case that leads them to blame Minnie Wright.