Apple's mobile phone doesn't show delivery. What's going on here?

IMessage account is not logged in correctly, and there is a lack of Wi-Fi or cellular data network connection.

1.iMessage account login is incorrect: To use the iMessage function to send and receive short messages, you must first log in to the iMessage account correctly.

2. Lack of Wi-Fi or cellular data network connection: In order to successfully send and receive iMessages information, you need to connect to an available Wi-Fi network or cellular data network.