By default the ordering of files is by ordering number descending and file name ascending. New files will always get a ordering number of 0. By assigning a number greater than 0 you can move individual image up. Usually one would name the image files like one would like to have them ordered in the front end and sorts special images on top of the list.
In the components options and for an individual local even you can define which column is used to sort the files in addition. This sort attribute is applied before the other sort attributes mentioned above. You can find the configuration in the Events - List tab in the components options.
The fields for entering ordering numbers for files will disappear if the event is sorted by anything else than the ordering column. Files appear in the same ordering as they would appear in the front end.
This option allows to display the images of an event in random order. You can switch it on in the components options (tab Events - List) or directly for an event using the sorting tab. Keep in mind that this option gets only active if the layout you use does not has a pagination bar. Random order and paging does not make much sense. Also, it does only effects the main component. Modules and plugins do not react on this setting.