For a comprehensive summary of all rolls and modifiers, see: Die Rolls
A Damage Roll happens when the game wants to determine the damage done by a successful attack, area of effect spell, trap, and so on. It can involve one or many dice of any type.
For example, a successful hit with a Dagger will lead to a d4 being rolled to determine the damage (referred to as 1d4 damage), whereas a successful attack with a Greatsword will lead to two d6 being rolled (referred to as 2d6) for a total damage of 2 to 12. Being caught in a Fireball will cause 8d6 points of damage, though a successful Saving Throw can reduce it to half.
For attacks made with weapons, various Modifiers can affect the total value of the roll, such as the attacking creature's Ability Score Modifier, Proficiency Bonus, or Advantage / Disadvantage. For the damage of spell attacks, no such modifiers apply.