Constitution is the measure of a character’s physical health, stamina, energy, and will to resist and endure.
A character’s hit points are affected by its Constitution modifier. At each level, a player rolls their class’s hit die and adds their Con modifier to determine how much HP they gain at that level.
Increasing your Constitution modifier retroactively increases your HP for former level-ups. For example, if your Con modifier goes from +3 to +4 at level 8, you would gain 7 hit points for the previous levels, and then roll your hit die and add your new (+4) modifier to determine your hit points gained for reaching level 8.
While no skills are related to Constitution, a DM could call for a Constitution check in situations like:
Holding your breath
Marching or laboring for a long time without resting
Going without sleep, food, or water
Drinking a powerful liquor
A creature can hold its breath for (1 + Constitution modifier) minutes. After that, it can survive for (Constitution modifier) rounds before dropping to 0 hit points.
So, with a +2 Con modifier, your character can hold their breath for 3 minutes and then survive for 2 rounds of combat before falling to 0 HP and making death saves.
This goes for drowning as well.
A party can only travel 8 hours in a day before they risk becoming exhausted. After 8 hours, players must make a DC (10 + 1 for each hour past 8 hours) Constitution saving throw or gain +1 level of exhaustion.
Examples of Constitution
Saving throw. In the desolate crypts, Aric Stoneheart confronted the nefarious necromancer, Morlak the Malevolent. As Morlak unleashed waves of enervating magic, attempting to drain Aric’s life force, the stout dwarf stood firm. Aric’s constitution, a testament to his indomitable spirit, resisted the necrotic assault. Gritting his teeth, veins pulsating with resilience, he advanced. With each step, he defied the deathly tendrils, his very essence repelling the insidious magic. Morlak’s dark laughter echoed, but Aric pressed on, an unyielding bulwark against the forces that sought to consume him.
Swimming. Beneath the azure waves of the Forgotten Sea, Lirael explored the sunken ruins. Lirael possessed a constitution that defied the crushing depths. With a lungful of air, she delved into the abyss, hunting for forgotten treasures. Lirael’s lungs burned, but her unyielding constitution allowed her to linger in the watery depths.
Marching all day. Across vast plains, General Thalia Stormheart traveled. From dusk till dawn, Thalia marched tirelessly to report the advance of the enemy’s unknown army, coming for Neverwinter. The Legion aimed to exploit exhaustion, but Thalia’s unmatched constitution defied weariness. Her iron will propelled her forward, overcoming fatigue.