Flip back to pages 54 and 55 of the Starter Set's adventure booklet, at the beginning of Appendix B: Monsters. This section explains how to read the monster's stats. I want to bring your attention in particular to the text in the heading Actions (p. 55, bolded phrase my emphasis):
Hit. Any damage or other effects that occur as a result of an attack hitting a target are described here. As DM, you have the option of taking average damage or rolling the damage; for this reason, both the average damage and the die expression are presented.
So "Hit 13 (2d8 + 4)" tells you what happens after you've already made a to-hit roll and it landed: an average of 13 damage, which is the average of 2d8 + 4 damage. You can either just deal 13 damage, or you can roll for it (but not both). The average is the same, so it's up to you. Since taking the average for damage isn't an option for players, no average is listed beside die expression for damage on character sheets and they always roll for it.
The "+X to hit" is what you add to the d20 roll to hit a target AC.
Putting this all together, you can interpret the notation on the character sheet too: "+4, 2d6 + 2 slashing" means that the attack roll gets +4 to hit, and (if it hits) does 2d6+2 slashing damage.