Here is a screen shot from Tim:
I tested it myself by typing my company name into Google search and since I was signed in to the Google account that manages my Google My Business listing, I also got the question.
It asks for the month and year but you can also specify the exact date, if you wanted to.
I don’t know where Google will use this information but they are now asking for it.
Some are saying there was a way to specify the open date in the old user interface but it was kind of hidden. I am not sure but now they are asking for this information in a very bold way.