In the sector Events may spawn at certain points on the map, Events are categorized into two sections: Special and Random.
Special events are static events that are manually made by developers (or modders) and as such they have predictable variables and outcomes. They are always the same and never change and spawn when certain conditions are met (EG Time, Relations, Fleet Size, Character Level, Location, etc.). For these they either are static in space or move along a pre-determined route. Typically these missions are for story use (what story there is that is). Special Events are marked with an exclamation mark.
Random events are a lot more chaotic, you may not know what you're getting into. Unlike Static Events they are "leveled" with the player, as to always be the right amount of challenge. They appear randomly every so often while within a sector. It could be ranging from being attacked by bounty hunters after you *** off a certain faction or recovering a lost ship all the way to dealing with crazy events like a ship graveyard that isn't as dead as it appears, or being attacked by unidentified alien space craft and other sci-fi non-sense that happens in space. Random Events are marked with a question mark to show that they're randomly generated.
When you put your cursor over an event it shows some basic data, recommended level/fleet size, type of hazards, rewards for completion, etc.