Skill checks use the modifiers of ability checks to be made. Some skills can have proficiency for a character which means they are better at it and gain a boost to the check.
Acrobatics(Dex)
Acrobatics covers your attempt to stay on your feet in a tricky situation, such as when you're trying to run across a sheet of ice, balance on a tightrope, or stay upright on a rocking ship's deck. An Acrobatics check can also be made to see if you can perform acrobatic stunts, including dives, rolls, somersaults, and flips.
Animal Handling(Wis)
When there is any question about whether you can calm down a domesticated animal, keep a mount from getting spooked, or intuit an animal's intentions, then it would be an Animal Handling check. You also make an Animal Handling check to control your mount when you attempt a risky maneuver.
Arcana(Int)
Arcana measures your ability to recall lore about spells, magic items, eldritch symbols, magical traditions, the planes of existence, and the inhabitants of those planes.
Athletics(Str)
Athletics covers difficult situations you encounter while climbing, jumping, or swimming. Examples include the following activities:
You attempt to climb a sheer or slippery cliff, avoid hazards while scaling a wall, or cling to a surface while something is trying to knock you off. You try to jump an unusually long distance or pull off a stunt mid-jump. You struggle to swim or stay afloat in treacherous currents, storm-tossed waves, or areas of thick seaweed. Or another creature tries to push or pull you underwater or otherwise interfere with your swimming.
Deception(Char)
Deception lets you convincingly hide the truth, either verbally or through your actions. This deception can encompass everything from misleading others through ambiguity to telling outright lies. Typical situations include trying to fast-talk a guard, con a merchant, earn money through gambling, pass yourself off in a disguise, dull someone's suspicions with false assurances, or maintain a straight face while telling a blatant lie.
History(Int)
History is your ability to recall lore about historical events, legendary people, ancient kingdoms, past disputes, recent wars, and lost civilizations. It could also be used to recall past memories that you might have forgotten.
Insight(Wis)
Insight is the ability to 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.
Intimidation(Char)
When you attempt to influence someone through overt threats, hostile actions, and physical violence, then it would cause an Intimidation check. Examples include trying to pry information out of a prisoner, convincing street thugs to back down from a confrontation, or using the edge of a broken bottle to convince an idiot to reconsider a decision.
Investigation(Int)
When you look around for clues and make deductions based on those clues, you make an Investigation check. You might deduce the location of a hidden object, discern from the appearance of a wound what kind of weapon dealt it, or determine the weakest point in a tunnel that could cause it to collapse. Poring through ancient scrolls in search of a hidden fragment of knowledge might also call for an Intelligence Investigation check.
Medicine(Wis)
Medicine lets you try to stabilize a dying companion or diagnose an illness, it can also be used to apply more careful medicine.
Nature(Int)
Nature measures your ability to recall lore about terrain, plants and animals, the weather, and natural cycles.
Perception(Wis)
Your Perception 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.
Performance(Char)
Performance determines how well you can delight an audience with music, dance, acting, storytelling, or some other form of entertainment.
Persuasion(Char)
When an attempt at influencing someone or a group of people with tact, social graces, or good nature, then it might be a Persuasion check. Typically, you use persuasion when acting in good faith, to foster friendships, make cordial requests, or exhibit proper etiquette. Examples of persuading others include convincing a shop owner to lower their price, negotiating peace between warring tribes, or inspiring a crowd of townsfolk.
Religion(Int)
Religion measures your ability to recall lore about deities, rites and prayers, religious hierarchies, holy symbols, and the practices of secret cults.
Sleight of Hand(Dex)
Whenever an attempt an act of manual trickery, such as planting something on someone else or concealing an object on your person, make a Sleight of Hand check. It might also be used to determine whether you can lift a coin purse off another person or slip something out of another person's pocket.
Stealth(Dex)
A Stealth check is an attempt to conceal yourself from enemies, slink past guards, slip away without being noticed, or sneak up on someone without being seen or heard.
Survival(Wis)
A Survival check is made to follow tracks, hunt wild game, guide a group through frozen wastelands, identify signs that monsters/creatures live nearby, predict the weather, or avoid quicksand and other natural hazards. A homebrew rule I made is that it also acts as Survival Instincts for dangerous situations.
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There are also tool checks that can only be made if you have proficiency with said tools. Examples being Herbalism kit to use herbs and create remedies, Smith's tools for smithing etc.