DnD 5e - Passive Skills
There are two passive skills: Passive Insight, and Passive Perception. In addition to using Insight and Perception actively, these skills also apply passively. You can actively use them both by taking the time to scrutinize a creature (Insight) or to look around at your surroundings (Perception), but just because you're not deliberately examining things doesn't mean that your eyes and ears snap shut.
In all cases, a passive skill is equal to 10 + your skill bonus with that skill. If you have Advantage on checks with that skill for some reason (maybe a spell or a magic item), your passive skill increases by 5. If you have Disadvantage (maybe it's foggy and you can't see well), your passive skill decreases by 5.
Because passive skills don't require you to do anything for them to work, it's often helpful for the Dungeon Master to know everyone's passive skills. This can help the DM to inform players when they notice something interesting without the DM constantly asking to peek at everyone's character sheets.
Passive insight represents your ability to discern creatures' motives and discern lies and deception without actively focusing on them. If a creature tells an obvious lie, or if they're a bad liar and you have high Passive Insight, you're likely to notice with Passive Insight.
Passive perception represents your ability to notice things going on around you. Hidden objects and creatures, subtle smells, little details, distant conversations, and any number of other things.