On the Google search results page, it tries to match your search with a local business, and show you its details on the right - a map, maybe photos, business hours, contact information, etc. I presume they pull this from a variety of sources.
One year, I noticed my library's details showing up there - phone, website, hours, etc. Great, that's Google making things easier for people to find us.
Except, later on our hours changed (we started being open on Sundays), but the hours on Google didn't change. Then one of our Trustees noticed it, asked my Director why our hours were wrong on Google, and that became my project for the day.
This was also what another nearby library recently asked me - their hours were listed on Google, but weren't correct, so how do you change them?
The answer is that you have to "claim" ownership of that business listing by going through the authentication process to prove you're actually entitled to make changes. This then ties the business listing to a Google account, which you can then log into to make changes. It's not hard, and as far as I can tell, is the only way to update it when things change - like if you're open on Sundays in the winter but not the summer, you've got to go in twice a year and manually make the change (lest your Trustees think you're not keeping up with your Internetly duties).
Anyway, here are some pictures. The one on the left is for the JV Fletcher Library (in Westford, MA), which has not yet "claimed" their listing. Ours, on the right, has been claimed - you can tell because theirs has the subtle "Are you the business owner?" link under it:
Once you click that link, you'll be prompted to log in and authenticate. It's been a couple years since I did this, and I don't remember exactly what the authentication process was - although, it could have also changed since then. I also don't entirely understand the hierarchy of various Google products, but I'm sure there is some relationship between business listing, Google accounts, Google+, and I don't know what all.
However, it's worth doing, to get your Google listing associated with an account you can edit. Because of course, if people see it on Google, they assume it's right - so if Google says you're open on Sundays, it's your fault if you're not.