Alerts can be in three states:
This is the default and main state and alert is in. When alert get created they are in the open state.
Only alerts in the open state show on the Project Overview page.
Users have the ability to snooze an alert to hide it from the Project Overview page. The issue behind a snoozed alert is still active however it is hidden from view.
Once an alert is no longer an issue either because the alert was turned off, the setting changed or the issue that caused the alert is no longer an issue the alert will be resolved. Once an alert is resolved the state cannot change. If the issue happens again there will be a new alert created in the Open state.
To learn more how alerts work check out these articles: