Examples might include:
Not to be confused with Dexterity (Acrobatics) though they might be similar in some ways, and you might be able to convince a DM that a movement requires the strength of an athletic feat, rather than the dexterity required for an acrobatic movement.
You're balancing on a rope, and your DM has had you make a Dexterity (Acrobatics) check to see if you can stay upright, you slip, and your DM makes you roll a Strength (Athletics) check to see if you grab the rope on your way down, and can hang on against the force of gravity.
The Strength Modifier is added to attack and damage rolls for strength-based weaponry.
Carrying capacity is Strength x15
Pushing, dragging, lifting, is possible up to twice the carrying capacity in pounds.
Each size category above medium doubles carrying capacity and push, drag, lift.
Tiny creatures halve their carrying capacity and push, drag lift.
Optionally, if you carry a total weight of Strength x5, you are encumbered.
If you carry a total weight of Strength x10, you are heavily encumbered.