Additions & subtractions to damage are any time when a feature, or item, or trait, allows a creature to directly increase or decrease damage. They do not apply if the recipient of the damage has immunity (such as a door and psychic damage), as immunity outright cancels/prevents damage of a type or types.

One example of decrease is the recent Interception fighting style from from Class Feature Variants UA, which allows a PC to reduce damage to an ally (or themselves) by 1d10+proficiency bonus as a reaction.

The text you quoted from Xanathar's Guide is basically an order of operations for damage, and you can read it like this for each type of damage in an attack/saving throw (slashing, poison, etc):

1- does the creature/object have immunity to this damage type? If **yes**, no damage can result of this type. If **no**, move on to step 2.  
2- does anything add to or subtract from damage of this type? Change the damage accordingly, then move to step 3.  
3- is there resistance to this damage type from any source? If **yes**, reduce this damage by half (rounded down), then move to step 4. If **no**, move on to step 4.  
4- is there vulnerability to this damage type from any source? If **yes**, double this damage, and apply. If **no**, apply figured damage.

You follow the above steps for each type of damage that might occur, which could be 2 or even 3 separate types of damage at once. But, it is much easier when you're playing to do this, than reading it might suggest.