What is a "Message center" when I look at my message detail of my text messages?

What does it say in a text from someone you know? Does their number show up as “message center”?

It’s basically the post office. :)

If I send you a message, the message will first be sent to the message center, then delivered to your cell phone when it can be reached.

This enables that, if your cell phone is off when I send the message, the message is delivered to it when you turn it on again.

For more info, check out this Wikipedia article.