In Trifles, why did Mr. Hale visit the Wrights' house?

Another aspect to Mr. Hale stopping in on the Wrights is that he hoped by talking about the party line in front of Mrs. Wright, John Wright would change his mind, though he notes, "I didn't know as what his wife wanted made much difference to John."  This quote shows that Mr. Hale, and perhaps the rest of the town, understood the dominance that John Wright held over his wife.  As the play continues, Mrs. Hale notes to the County Attorney that she has not set foot in the house in well over a year, so the fact the Mr. Hale stops by begins to seem even more unusual, that he would just stop in on a whim to see about a party line in the house.  

In Trifles, why did Mr. Hale visit the Wrights' house?

Mr. Hale goes to John and Minnie Wrights' house because he wants to talk to John about sharing a party phone line.  During the play's time setting and because of the isolated area, it was not uncommon for neighbors to have a party line.  If you have seen old movies where the residents of a house or apartment have to connect to phone numbers through an operator, this is what a party line is like.  Mr. Hale needs the Wrights or another neighbor to share the line with him so that it will be affordable and practical.

While this might seem like an insignificant incident in the play, it is actually quite important.  John Wrights' negative attitude toward have a phone line installed demonstrates the extent to which he has isolated his wife.  Not only do the Wrights live far away from others, but John has also hindered Minnie from being involved in normal social activities (singing at church).  His denial of yet another means of outside human contact coupled with his killing the one thing that brings Minnie joy (her bird) prove too be the final impetus for Minnie to kill him.

Why did Hale visit John Wright's farmhouse in Trifles?

A party phone line is a kind of shared telephone service. These were very common in rural areas at the time that Trifles is set. Cost-effective, economical, and practical, they were often the only way that people living in remote areas could gain access to telephone communication.

The setting up of such a party line was the reason for Mr. Hale's visit to John Wright's farmhouse on the day he learned Wright was dead. Hale clearly understood the benefits of the party phone line. When he had spoken to John Wright about this in the past, however, Wright had been less than enthused, and it's not hard to see why. Wright obviously realized that if a telephone line was set up at his farmhouse, then his wife, Minnie, would become less isolated, more open to the outside world—and that's the very last thing he wanted. Nevertheless, on the day Mr. Hale learned that Wright had died, he had come to speak to him about this matter again.

Wright had already shown that he was more than willing to restrict Minnie's social activities, such as singing at church. He likely knew that the more human contact Minnie had, the more difficult it would be for him to control her life. Preventing the setting up of a party line, therefore, would have been to Wright's advantage, as it would preserve Minnie's isolation, thus preserving Wright's control over her. And in symbolic terms, this also serves to remind us of the lack of communication between Mr. and Mrs. Wright.