Random Events are events that you will simply find in the world. Just head to the starting intersection or location to begin them. Be sure to watch your radar while hunting these. Blue and Red Blips will appear on it to indicate some of the events beginning. They can be trigger by all characters unless stated otherwise.
Of the 46 Random events in the world, 57 with all the stores, ATM and Armored Car heists. Only 14 need to be completed to count toward the 100% completion. They comprise 5% of your overall completion.
After you have completed the mission Nervous Ron, you have an additional option. With any of the hitchhikers or drunk escorts, . Any of these people can be brought to the Altruist Cult Camp. It is marked by an "A" on your map. If you bring 4 of them there, that will trigger the Altruist Shootout