Wisdom reflects how attuned you are to the world around you and represents perceptiveness and intuition.

A Wisdom check might reflect an effort to read body language, understand someone’s feelings, notice things about the environment, or care for an injured person. The Animal Handling, Insight, Medicine, Perception, and Survival skills reflect aptitude in certain kinds of Wisdom checks.

When there is any question whether you can calm down a domesticated animal, keep a mount from getting spooked, or intuit an animal’s intentions, the GM might call for a Wisdom (Animal Handling) check. You also make a Wisdom (Animal Handling) check to control your mount when you attempt a risky maneuver.

Your Wisdom (Insight) check decides whether you can determine the true intentions of a creature, such as when searching out a lie or predicting someone’s next move. Doing so involves gleaning clues from body language, speech habits, and changes in mannerisms.

A Wisdom (Medicine) check lets you try to stabilize a dying companion or diagnose an illness.

Your Wisdom (Perception) check lets you spot, hear, or otherwise detect the presence of something. It measures your general awareness of your surroundings and the keenness of your senses. For example, you might try to hear a conversation through a closed door, eavesdrop under an open window, or hear monsters moving stealthily in the forest. Or you might try to spot things that are obscured or easy to miss, whether they are orcs lying in ambush on a road, thugs hiding in the shadows of an alley, or candlelight under a closed secret door.

This all seems rather straightforward but there are some edge cases that can complicate things. First of all, how much can be detected with passive Perception? Passive Perception acts as a lower floor for a Perception check. It's always on, even if a character attempts an active Wisdom (Perception) check. It's the minimum of what they see. You can compare the DC to detect the trap with each character's passive Wisdom (Perception) score to determine whether anyone in the party notices the trap in passing. Sometimes characters have very high passive Perception scores. The observant feat can boost it even higher. Obviously we don't want to negate this bonus. Players chose these options in particular for their characters.

But we can change what they see with passive Perception. This depends on the story and the situation. A character with a passive Perception higher than the DC of a trap notices danger ahead, but they might not know what danger they see. This requires its own Intelligence (Investigation) check to learn more about what is going on with the trap. Like passive Perception, a passive Investigation likely acts as a lower floor for investigating the mechanics of traps. Again, we decide what information comes up from this. Yes, you see danger ahead (high passive Perception). Yes, you see that there are deep grooves surrounding some of the tiles in the floor ahead and believe they move or can be moved (high passive Investigation). That doesn't tell you exactly what is going on but smart characters (and smart players) will test it out and see. Maybe they back up and toss something heavy on the tile. Maybe they duck out of the way and press a torch down on it only to see a poisoned barbed dart hit the torch. They still learn things by actually investigating.

One note about passive Perception — lighting matters a lot. Dim lighting for those without darkvision drops passive Perception by five. The same is true for total darkness and those with darkvision. Keeping track of the lighting tells you how easily the characters can actually perceive. We're not monsters, though. We should likely mention this difficulty before the characters start wandering into pit traps. “The total darkness in this chamber makes it difficult to see well, even for those of you with darkvision.” Give them the reminder and they'll likely need to fire up some light to avoid the penalty to their passive Perception.

The DM might ask you to make a Wisdom (Survival) check to follow tracks, hunt wild game, guide your group through frozen wastelands, identify signs that owlbears live nearby, predict the weather, or avoid quicksand and other natural hazards.

The GM might call for a Wisdom check when you try to accomplish tasks like the following:

• Get a gut feeling about what course of action to follow
• Discern whether a seemingly dead or living creature is undead

Clerics, druids, and rangers use Wisdom as their spellcasting ability, which helps determine the saving throw DCs of spells they cast.
Source PHB 2014 https://slyflourish.com/flow_of_trap_detection.html