Datadog refers to events that are generated from triggered monitors as Incidents. They're also known as a Monitor Alerts.
The best way to identify these in the Events page is to select the corresponding filter in the filter list:
Incidents are unique to regular events and annotations in that they can be claimed/acknowledged by clicking the claim button (shown below) on the parent event or putting a
#claim in the comments.
By claiming an event a user is essentially assigning it to themselves and signaling to other users that it is being investigated. As an indicator of this, Datadog will pin the user's name and portrait to the record.
Once claimed, an incident can be resolved by clicking the resolve button indicating to the team that the underlying issue has been addressed: