What is the significance of wedding ring?

The wedding ring is a major clue because it was taken off and removed.... and yet, the other ring was returned to his hand.

“Then the murderer, or whoever it was, first took off this ring you call the nugget ring, then the wedding ring, and afterwards put the nugget ring back again.”

In addition to the other items, Holmes believes that the entire affair is possibly a set up.

“The open window, the blood on the sill, the queer card, the marks of boots in the corner, the gun!”

“Nothing there that could not have been arranged. Mr. Douglas was an American, or had lived long in America. So had Mr. Barker. You don’t need to import an American from outside in order to account for American doings.”

The wedding ring is kind of hint which is when everyone was investigating to Mr.Douglas so there was a ring which was lost so that was a wedding ring

It holds important significance as Mr.Douglas wore 2 rings,one snake ring (or nugget ring in some editions)and his wedding ring,in order for it to go missing one must remove the snake ring,then take the wedding ring and put the snake ring back again,through this it was perplexed that if this theory was right then the culprit could be mr.barker who was too much frank with mrs.douglas this planted a suspicion that he killed mr.douglas to marry her or it could be that the whole thing was staged the dead may not be douglas because the wife ,Mrs.Douglas did not cry or wanted to see the face of her dead husband.

The wedding ring was missing which stipulated that the murder is somehow related to Mr Douglas's marriage. According to Ames, the chief servant of Birlstone Manor, Mr Douglas always wore his wedding under his twisted snake ring (or nugget ring as some people say). He never wore it off, so the dissapearance of the wedding ring was something to be noted for investigation and better understanding of the murder mystery case.