Every character has certain skills, saving throws, weapons, and abilities where they’ve gained proficiency by training and through virtue of their background.
When making a d20 roll using these abilities, each character gains a special bonus which is called their proficiency bonus. This is a number that’s shown in the class table of D&D sourcebooks for each and every class.
A Proficiency bonus is based on a character’s total level, not their class levels.
For example, every character that reaches level 5 total receives an increase in their proficiency bonus from +2 to +3, regardless of whether they multiclassed.
The proficiency bonus is added to a number of different types of checks, but only if the character has proficiency in the right skill or ability. These checks include:
(a) Weapon attack rolls (b) Spell attack rolls (for casters) (c) Spell save DCs (for casters) (d) Saving throws (e) Skill checks (technically this is a type of ability check) (f) Tool use checks (this is also a type of ability check)
It’s common for 5e to base other abilities on a character’s proficiency bonus, too.
For example, a Battle Master Fighter’s Maneuver Save DC is based partly on their proficiency bonus, while a Phantom Rogue has certain abilities that they can use a number of times per day equal to their proficiency bonus.
Note: a character does not gain a proficiency bonus to their AC when using armor or shields that they’re proficient with, although there are downsides to using armor and shields if you’re not proficient. Such as a slower movement speed or the inability to cast spells.
Also, per the Player’s Handbook:
For example, take Morgana: a Level 1 wizard.
She’s proficient in daggers, darts, slings, quarterstaffs, and light crossbows, with +2 proficiency bonus.
Her strength is 10 (+0), dexterity is 16 (+3) and Int is 16 (+3).
– Morgana can attack with a dagger using dexterity, since it is a finesse weapon, for a total of +5 to hit (+3 for Dex modifier, +2 for proficiency), with damage of d4+3 (note, proficiency bonus is not added to damage).
– Similarly, Morgana could use a light crossbow for +5 to hit, with d8+3 damage.
– If she attacks with the quarterstaff, she needs to use strength (+0), but she can still add her proficiency bonus, for a total of +2 to attack. The damage is d6, or d8 if she takes advantage of the versatile property.
– Morgana could use a rapier, which also has finesse property, even though she is not proficient with a rapier and cannot add her proficiency bonus to the attack roll. She has a +3 to hit from her dexterity and does d8+3 damage.
– In theory, Morgana could fight with a Great Sword. But since she has a low strength (+0) and is not proficient in the great sword, her attack roll bonus would be +0 and her damage would be 2d6.
– Morgana could also attack using a cantrip like fire bolt, which would have +5 to hit (Int modifier + proficiency bonus) and do d10 damage.
– Or she could cast Toll the Dead, which has a Spell Save DC of 13 for her target (8 + int modifier + proficiency bonus).