A weapon with the Finesse property allows you to use your Dexterity modifier instead of Strength to determine the attack and damage bonuses. A finesse weapon with the “Thrown” property can also use Dex for attack and damage rolls.
If you look at the list of weapons in the equipment section of Chapter 5 of the Player’s Handbook, you’ll notice that several weapons have special properties. “Finesse” is one of these special properties for some weapons.
Basically, finesse weapons tend to be heavily favored by Dex-based characters, like Rogues.
For example: a level 1 fighter with Dex 16 (+3) and Str 12 (+1) might want to compare a long sword (d8 damage, no finesse) to a rapier (d8 damage, with finesse). The fighter has +2 proficiency bonus, which applies to the attack but not to damage.
When using the longsword, the fighter has +3 to hit (+1 from strength, +2 from proficiency) and does d8+1 damage.
Using the rapier, the fighter has +5 to hit (+3 from dex, +2 from proficiency) and does d8+3 damage.
Clearly the rapier is the better option. In theory, the fighter could use STR for their rapier attacks and damage, but that doesn’t make much sense in this case.
There are a limited number of finesse weapons in 5e, and they tend to do a bit less damage (1 or 2 points less on average) than non-finesse weapons.
Most finesse weapons also lack the properties that some of the more powerful 5e weapons have, such as Reach and Heavy (which meshes well with the Great Weapon Master feat).
A list of the finesse weapons in 5e:
Dagger
Dart
Rapier
Scimitar
Shortsword
Whip
For characters with martial weapon proficiencies, here’s some weapon choice tips to keep in mind:
If you want to wield one weapon, use the rapier.
If you want to wield two weapons, use shortswords or scimitars.
If you want to melee attack from 10’ range, use a whip.
If you want to attack from range, you’re probably better off using a longbow or crossbow.
