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.