What does a magic weapon's plus apply to?

Question

When a PC finds a +1 weapon, what stat or stats increase by one? For example, in the Lost Mine of Phandelver adventure in the Starter Set, there is a +1 Longsword. What does it do?

Answer 1

From the Basic D&D DM book p60

Weapon, +1,+2,+3

You have a bonus to attack and damage rolls made with this magic weapon. The bonus is determined by the weapon’s rarity

So you get a bonus to your attack and damage rolls with a +1 weapon.

Answer 2

Flip your Lost Mines booklet to "Appendix A: Magic Items" on page 52. The "Item Descriptions" heading tells you how to read magic item descriptions. The "+1 Weapon" subheading says in part (same page, emphasis mine for clarity):

You have a +1 bonus to the attack rolls and damage rolls you make with this weapon.

Answer 3

No "stat" receives the bonus. In some other game systems, it may be common for magic weapons to also give a bonus to a stat, or indeed only to a stat, but in D&D a magic item "+1" has generally meant that it provides the bonus for using that item.

For items that are actively used, that means directly to the checks made with that item for that item's intended purpose; for a weapon, that's +1 to attack and damage, as others have said. Absent clarifying remarks in the source material, I would also expect a set of "Lockpicks +1" to give that bonus to attempts to pick locks; magical "Rope +1" I would expect to confer that bonus to any check to use the rope (e.g., to tie it to something, possibly before climbing with it). The climb itself, though, is not construed as using the rope, so "Rope +1" would not necessarily help the climb check; on the other hand, "Rope of Climbing +1" I would expect to only provide the bonus to the climb check made with the rope, because "Climbing" is that rope's stated intended purpose.

Passive magic items work only slightly differently; they add to whatever target number an opponent must meet when they are making a check. The most obvious example of that being armor; magic Armor +1 adds the bonus to the wearer's Armor Class.

There are items that modify stats directly, but they are explicit about doing so.

Answer 4

If it's a +1 sword then you get a +1 to each attack. When you roll damage you'd get a +1 to each damage roll.
Basic Rules page 170

Weapon, +1, +2, or +3
Weapon (any), uncommon (+1), rare (+2), or very rare (+3)
You have a bonus to attack and damage rolls made with this magic weapon. The bonus is determined by the weapon’s rarity

The rarity is indicated by the italics.