If you have more than one Apple device, you likely want them to be synced. Messages are one of those things. By default, they are set to not sync between devices. Fortunately, it is easy to change.
In iOS (12 or later) you open Settings > [your Apple ID] > iCloud. Activate iCloud syncing for Messages. Do the same on all your devices. If you are connected to Wi-Fi you will see messages from other devices popping up almost immediately. Otherwise, they will start syncing next time you connect to a wireless network.
Do you have more than one Apple device, like iPhone, iPad, iPod, Mac or Apple TV?