Whats the main advantage and disadvantage of "do not keep activities" in android

How much this option will affect mobile applications?

If they are well writen this option will not affect them.

What exactly does this do?

If you have this option turned on only variables kept in activity with method onSaveInstanceState will be saved when you go to another activity or app goes in background. All other variables will be removed immediately. When this option is off there is possibility that these variable will be kept

Does that mean if I open an app and as soon as I leave it, it actually closes that app and I wouldn't see it in the task manager to manually kill it?

No it means that all not kept variables will be removed. When you in example press home button.

Does this create any positive and or negative functionality on my apps?

No it only helps to develop application properly. It helps to predict unexpected situations.


Do not Keep Activities is purely a developer option that will help you to check if

  1. You have Saved the state of the activity, before it goes background.

2̶.̶ ̶H̶a̶n̶d̶l̶e̶d̶ ̶L̶o̶w̶ ̶M̶e̶m̶o̶r̶y̶ ̶S̶i̶t̶u̶a̶t̶i̶o̶n̶s̶ ̶p̶r̶o̶p̶e̶r̶l̶y̶(̶i̶n̶ ̶w̶h̶i̶c̶h̶ ̶c̶a̶s̶e̶ ̶t̶h̶e̶ ̶a̶c̶t̶i̶v̶i̶t̶y̶ ̶w̶i̶l̶l̶ ̶b̶e̶ ̶d̶e̶s̶t̶r̶o̶y̶e̶d̶)̶.̶ ̶

Edit : This option does not emulate Low memory Situations. When the device experiences low memory, the system might ask the activity to Drop by calling Finish() or it may go ahead and kill the process completely, as the comment says.

It is still good to develop with this option enabled. You will have to properly code the onSaveInstanceState() and onRestoreInstanceState() methods. By doing this, even if the process gets killed, when the user navigates back to this activity, onCreate() will be called with the savedInstanceState that was saved in the onSaveInstanceState(Bundle) method.


ADVANTAGE :

Developer can check the abnormal behaviour of their application and fix the cases of low memory - framework kills the application

DISADVANTAGE :

If user has unknowingly enabled this option, then the device will work slow and every activities will be re-created across user navigation on his device. This will hinder user work

Very good answer is given in xda developer forum about usage of this option