Two-Weapon Fighting
Attack with a light weapon in each hand: bonus action attack with the offhand, but no ability modifier to damage unless you have the Two-Weapon Fighting style.
Dual wielding allows a character to make an extra attack with a second weapon as a bonus action, at the cost of some limitations.
Requirements
When you take the Attack action and attack with a light melee weapon held in one hand, you can use a bonus action to attack with a different light melee weapon held in the other hand. Both weapons must have the light property (e.g., shortswords, daggers, scimitars, handaxes).
Damage Modifier
By default, you do not add your ability modifier to the damage of the bonus action attack. You still add it to the attack roll as normal. The Two-Weapon Fighting fighting style (available to Fighters and Rangers) overrides this, allowing you to add your ability modifier to the bonus attack's damage.
Interaction with Extra Attack
The bonus action attack from two-weapon fighting is separate from the Extra Attack feature. If a 5th-level Fighter attacks twice with the Attack action using their main hand weapon, they can still use their bonus action to make one additional attack with their offhand weapon.
Drawing Weapons
You can draw or stow one weapon as part of your free object interaction each turn. Drawing two weapons requires either two turns or the Dual Wielder feat, which also removes the light weapon requirement and grants +1 AC when wielding two melee weapons.
Limitations
Two-weapon fighting competes for your bonus action, which many class features also use (e.g., Bardic Inspiration, Cunning Action, bonus action spells). This opportunity cost makes dual wielding less attractive for certain builds.