Mr. Wright is the man found dead in his home. His wife is Minnie Wright, the main suspect in his murder. But Martha Hale also refers to her as Minnie Foster. This was her maiden name. Her married name is Minnie Wright. This is symbolic because Mrs. Hale remembers her as the more vibrant person she knew before she married Mr. Wright. Note the irony that this man was a lousy husband and his name is Mr. Wright, a homophone for "Mr. Right."
Mrs. Hale and Mrs. Peters conclude that Mrs. Wright (formerly known as Mrs. Foster) was like a caged bird in her marriage to John Wright. They suggest that John Wright was a hard man to live with and Mrs. Wright's freedom and happiness in life suffered as a result. In examining the dead bird, they confirm that somebody had wrung its neck. Most likely, it was John Wright. Although Mrs. Hale and Mrs. Peters do not approve of killing a man in his bed, they sympathize with Mrs. Wright. This is why they hide the dead canary. As dense as the sheriff and attorney are in their investigation, finding a bird with its neck wrung would be evidence and a motive that they could use against Mrs. Wright who essentially killed Mr. Wright in a similar way.