When on foot, not in combat and not in a mission or activity, someone can call The Protagonist and inform him that some gang is attacking some location and that The Protagonist should go and help protect the location. At that point a marker will appear on the map. The player is still free to start a usual mission or activity, or to save the game. Saving does not remove the marker, but reloading that saved game will.
Source: Saints Row Wiki, "Survival" article
If you're playing on the PC, you can get more frequent calls offering Survival missions by installing the Realism mod. Related changelog: "Calls from survival missions are now more frequently".
If you only want the Realism mod's feature to make Survival diversions more frequent and not its other changes, you only need to install its
sr3_city_survival.xtbl file (you'll need to extract it first or download it here), not install its other files, and put
sr3_city_survival.xtbl in the SR3 root directory.