Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
iMessage Suffering World Wide Outage
A lot of you have have been in touch to let us know that it appears Apple is struggling with an iMessage outage.We have had reports from around the world that iMessages are not sending also Facetime is inaccessible. Apple has commented saying they hope to have all services up and running again as soon as possible and we expect to hear from them very soon.
You can follow us on Twitter by following @macreviews and we will let you know as soon as the service returns to normal
We are also on Facebook and post regular fixes for bugs and breaking Apple related news.