What does the half-moon icon in front of the text message received by iphone mean?

That's because you turned on the iPhone's do not disturb mode.

Do not disturb mode in iOS is a very user-friendly setting, which belongs to the notification bar. It is also mainly set in the notification options. After clicking the notification, you can see the relevant options of do not disturb mode. When Do Not Disturb mode is enabled, the moon icon will appear in the status bar at the top, and incoming calls and reminders will be set to mute.

When enabled, the moon icon will appear in the status bar at the top, and incoming calls and reminders will be set to mute. This is the icon for Do Not Disturb mode:

Extended data:

Do not disturb the mode setting:

Set time: It means that you can set a time period. If Do Not Disturb mode is enabled, incoming calls will be muted during this time period, and incoming calls outside this time period will not be muted.

"Allow these people to make phone calls" in the Do-Not-Disturb mode: It is aimed at people or groups who are set not to mute their calls and avoid those strange calls. Anyone, everyone and individuals can choose. And all the contacts, family members and other groups.

References:

Do not disturb mode _ Baidu Encyclopedia