DnD 5e - Dexterity
Dexterity measures a character's nimbless, their agility, and their fine motor skills. A character with high Dexterity is able to avoid attacks in combat, evade area effects like dragon's breath and explosions, move stealthily, perform feats of acrobatics, pick locks, and use both light, nimble melee weapons like daggers and rapiers and ranged weapons like bows and crossbows more effectively.
Dexterity is most important for characters who fight using light weapons like dagger, finesse weapons like rapiers, and ranged weapons like bows. Bards, Monks, Rangers, and Rogues frequently have high Dexterity. Sometimes other classes, including Fighters, Paladins, and Warlocks also have high Dexterity.
Acrobatics, Sleight of Hand, and Stealth are all tied to Dexterity.
Acrobatics measures a character's ability to perform impressive acts of nimbless which typically require coordinating your entire body, such as staying upright on a slippery or icy surface, walking across a tight rope, or performing stunts like somersaults.
Acrobatics can also be used to escape grapples. If you perform a long jump (see Movement, later in this guide) and land in difficult terrain, you can attempt a DC 10 Dexterity (Acrobatics) check to avoid falling prone when you land.
Sleight of Hand
Sleight of Hand covers acts of manual trickery such as picking pockets, planting objects on a person unnoticed, and things which today might be described as "Up-Close Magic".
When you make a Sleight of Hand check, you typically roll against another creature's Passive Perception score, and you avoid notice if you succeed.
Stealth, as you might expect from the name, covers a character's ability to hide themselves or objects, to move about unnoticed, and to be generally stealthy.
When you make a Stealth check, you typically roll against another creature's Passive Perception score, and you avoid notice if you succeed. If the creature is actively looking for you, you roll a contest: the creature rolls Wisdom (Perception) against your Dexterity (Stealth).