In 5th edition, passive perception is sort of the default based on normal "awareness." So like, walking through the market to buy some apples, the pickpocket would have to roll against your passive perception to steal from you without being noticed. In this case, the characters passive perception score would a base of 10, plus 2 for WIS, plus 5 for the observant feat, resulting in the 17 passive perception score.
But if you know that market is filled with pickpockets, you might tell the GM that you're paying close attention to your pouches while on your way to the apple cart. That's the kind of thing that would probably translate to an "advantage," and according to page 175 of the PH, having advantage grants a +5 to passive scores. This would result in a passive perception of 22, making the pickpocket's job harder now that his target is specifically watching out for this kind of thing. The possible downside is that perhaps the players focus on watching for thieves results in missing something else that happens nearby.
I bring this up because GM's with experience in older editions would probably handle the second scenario with opposed checks, rather than using the built in passive mechanic as intended. So then you have a pickpocket stalking his target, and the target rolls bad on perception, resulting in weird situations that don't always make sense. Passive score, and perception in particular, are meant to handle this in the first place.
The whole thing is meant to avoid weird situations of the past where the guy is walking through the market, and the GM asks for a perception roll. He fails, and now the player is wondering what that was all about, and starts getting suspicious or paranoid, even though his character has no clue something is wrong.
Finally, in the time where you do need to make active perception checks for some reason, like if a player wants to search a room for a hidden key with a DC 15, it's totally possible that they fail even though their passive perception is higher. Why does that make sense? How many times have you gone searching for something in your house, like keys, tearing the place up because you *know* you put them on the counter when you got home, only to give up and find them 2 hours later in the clothes hamper? Those kinds of things do happen.
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