Google is continuing its marathon of updates with Googe My Business. After including a feature that allows business to start a free Google hosted websites directly from my business as well as updating the business posting features to all users, Google has come up with a new update for Google My Business: allowing users to send messages but also receive messages directly from Google My Business's dashboard.
This is update is currently rolling out in the United States and I bet it will soon be a world wide feature after the US update is successfully completed. Source: http://searchengineland.com/google-begins-rolling-messaging-feature-within-google-business-278790
Once you turn On the message with customers feature you will need to configure your phone number with Google Allo service: https://allo.google.com/ - the customers will actually use their own native messaging app.
From what I understand you are also able to receive and respond to these messages via standard SMS
Overall I'm wondering how beneficial such a feature would be for a real business. Keep in mind that you will have to respond to these messages sent by potential clients as fast as possible if you plan to respond 24 hours after the question or message was submitted the potential buyer would have certainly moved on to a competitor.
So, you will have to be available at any hour once you turn this feature on. Or you can assign somebody in your company to deal with this messages. I think this feature will grow very popular especially on local businesses where people may don't want to call but will certainly find easier the idea of writing a short message to you.