The Events Block shows a list of the upcoming events. There are two sections in this block: General Events and Personal Events. General Events feature those that have been entered in the site calendar normally. Once you add the Events to you personal calendar, you can see them in the personal section.
Strictly speaking, this block is not part of Geeklog itself, as it is actually provided by the Calendar Plugin.
The timespan that is displayed can be set in the Calendar Plugin's configuration.
As of 1.3.9, there is no standard feature that switches off the section name in case you dont have a personal event or the personal calendar is switched off.
The events that are shown depend on the permissions the current user has.