What does No SIM mean on my iPad?

It means the parts of your iPad responsible for reading the SIM card have failed. It's happening to a lot of people with iOS 7.

I downloaded iOS7 a few weeks ago and now have the No Sim messege. What can I do to fix it ?

I had this message on my iPad, I held the turn off button so it shut it down waited a couple of seconds turned it on again and my sim was working. Hope this helps.

Thank you, thank you! It worked🙂