As you go about your daily routine your phone periodically performs a 'handshake' with your phone provider's nearest transmit/receive mast. The phone sends a packet of data to the mast, and the mast responds - that way your network provider always knows which cell you are in.

When someone sends you a text the network mast nearest to you sends a signal to your phone, telling it that there's a text waiting. The phone responds,and the message is transferred. Once that happens the message no longer exists on the network - it's stored on your phone. The network records the time of the transfer, and it does the same thing if you send a text to someone else.

If your phone isn't switched on when a text arrives the network will hold it - sometimes for a few days - until your phone next makes a handshake. Sometimes the networks are very busy, and the high traffic may prevent the system from delivering your text. In this case the message will be buffered, and delivered when the network has the necessary bandwidth available. This can mean that some texts are delayed by a few hours, or even a day or so.

You can keep a text on your phone for as long as you like.