A simile makes a comparison between two things using the words "like" or "as." The purpose of a simile is to help the reader better understand an idea by making a comparison to something she already understands well.
In this simile, the person's relationship to the television is compared to a dance. Because the dance is "stiff" and "embraceless" we get the impression that it is awkward and strange. I'm reminded of middle school dances where everyone is afraid to dance or to touch his or her partner. Thus, the relationship with the television is tense, perhaps unwelcome. She does not love the television, but she still feels compelled to watch it.
In Amy Tan's novel, The Joy Luck Club, focuses on the many ways that the Chinese immigrant mothers often feel trapped by or uncomfortable with American culture. Since the television is a common symbol of American culture, we might take this simile further to suggest that it represents the woman's discomfort with the unfamiliar expectations of American society.