The Proficiency Bonus is a modifier applied to various Die Rolls based on the total Level of a creature (e.g, a Level 2 Monk/Level 3 Barbarian character will have a total level of 5). It can affect Attack Rolls, Saving Throws, and Skill Checks, if the creature has the correct type of Proficiency for the situation. It doesn't apply to Damage Rolls.
On the other hand, a Wizard normally only has Proficiency in Daggers, Quarterstaves, and Light Crossbows, so the Proficiency Bonus won't be added to attacks made with any other weapon, unless the Wizard has Proficiency in that weapon for some other reason.
For spells that require an Attack Roll to hit, the Proficiency Bonus is added if the creature has the innate ability to cast spells. (Note: As of Early Access Patch 9, all classes receive their Proficiency Bonus when casting a spell from a Scroll or other item, even when not innately able to cast spells.)
Saving Throws are categorized by Ability Score, such as Strength Saving Throw, Dexterity Saving Throw, and so on. For the Proficiency Bonus to be applied to a Saving Throw, the creature must have Proficiency in the corresponding type of Saving Throw. Each Class provides two Saving Throw Proficiencies. For example, the Fighter has Proficiency in Strength and Constitution Saving Throws, whereas the Wizard has Proficiency in Intelligence and Wisdom Saving Throws.
An Ability Check that is based on a Skill such as Athletics, Perception, or Sleight of Hand, is called a Skill Check. If a creature has Proficiency in the corresponding Skill, its Proficiency Bonus will be added to the roll.
Following is the value of the Proficiency Bonus, based on the total Level of the creature making the roll:
|1 to 4||+ 2|
|5 to 8||+ 3|
|9 to 12||+ 4|