Fine. That's better.
First, just to make certain there is no misunderstanding, when I say "Passive" I mean "always on, in the background". If you're interacting with someone who lies to you, you always have a BS-detector going. Something perhaps just doesn't jive or feel right, it is your instinctive "gut feeling." Empathy and understanding how someone else is feeling or understanding what their goals might be is also passive and involves Insight.
In the same respect, Perception is your senses. They are also passive ("always on"). If I am having a conversation and someone nearby opens the door, I will probably still hear it, just as if someone steps on a squeaky floor board, etc.
By making these passive, I can have them contested by things like Influence (Deception or whatever) and Stealth (to move quietly). If the rolls fail to beat the passive scores, the PC senses something is going on. In the case of Insight, perhaps the person trying to influence you is lying, or telling the truth but has ulterior motives, or whatever. In the case of Stealth, the "sneaker" is possibly heard or seen depending on the environment and situation.
If your passive scores beat the roll, you can use Investigation to learn more. Now, you are trying to read the tells of the person. Are they simply lying? Holding back information? Have a different agenda? Why are they trying to influence you? Against Stealth, do you see the sneaker or just a form and know something is there? Which direction did the sound come from? How far away was it? In short, Investigation is used to gain more information than your passive scores reveal, and it is an active attempt to discern that information.
For example, suppose two guards are on watch with WIS 10 and 12. You make a Dexterity (Stealth) check to sneak past them in the nearby shadows. You roll a total of 11, beating one guard by not the other. You overhear one guard, "Hey, did you hear that?" "No," replies the other.
But at this point, I as the DM, can have both guards roll Intelligence (Investigation) as they remain quiet, listen intently, and scan the shadows to determine if they see anything out of the ordinary. I roll for both and get 12 and 15, both beating your stealth. Now, they either heard you or saw you (perhaps something metal glinted off of the moonlight) and you see them moving towards you. What will you do???
If they had failed on their investigation rolls, you would have remained quite enough and/or hidden enough they didn't notice you, and so would resume their guarding and you could move on successfully.