DnD 5e - Strength
Strength measures a characters ability to exert physical force. A character with high Strength can lift heavier objects, carry more gear without being overloaded, break things with brute strength, shove and grapple creatures more effectively, and is more accurate and more effective with melee weapons.
Strength is most important for characters who fight in melee using heavy weapons like longswords and greataxes. Barbarians, Fighters, and Paladins frequently have high Strength.
Athletics is the only skill tied to Strength.
Athletics covers a large number of physically strenuous activities, including climbing, jumping, and swimming. While you can typically perform these activities without making an ability check, the DM may call for an ability check when the circumstances make the activity difficult. For example: You don't typically need a Strength (Athletics) check to climb stairs, but you might need one if you are climbing a sheer cliff. Similarly, you don't need a Strength (Athletics) check to swim across a still, shallow pool, but you might need to make a check if you are attempting to swim across a rushing river.
Athletics is also used for shoving and grappling, both of which will be covered in the Combat section, later in this guide.