This tab is a good place to check in first place if anything went wrong. It keeps records of all alerts and errors in Management Console's, agents' or jobs configuration. Events are distinguished by Component and Source.
Can be Management Console itself or an Agent, depending on where the error appeared.
Clicking on an agent name opens the agent's details view.
It can be "Global" or a specific job.
Component "Global" means that the event affect the overall Agent's misconfiguration. For example, agent's listening port if busy by another progress.
If the error affects a job execution, corresponding job run name appears as Component.
Component can be empty for "Management Console" source.
Events are simply records of what happened. They remain in the events list from Console's UI even though the error or misconfiguration itself might have already been fixed.
All events are also stored locally on Management Console server in its storage folder in data\reporting\daily subdirectory. These are sqlite database files with two timestamps in their name: start and end of a record. By default each db file keeps record for a day, new db is started next day, and is deleted 365 days later.
Manually deleting a database file clears the events from Console's UI.
Most frequent Events messages are explained here.