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.
To understand this, consider the relevant definition for immune, the basis of immunity: "not affected or influenced by something." So, if something has immunity to a damage type, then it isn't affected by that type; if it isn't affected, then any changes to the quantity have no effect, so you dont consider those changes.
This is why immunity consideration is the first step, because it tells you if the result is guaranteed to be zero or not.
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, and if any remains, 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 any remains. 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.