There are no such things in D&D 5e, at least not in a way that would be familiar from experience with previous editions.
Special Traits are explained on the following page in the Monster Manual. Special Traits are, well, special: they are abilities designed specifically for that creature and are defined per-creature in the creature's entry.
Immunities and damage resistance special traits tend to be a straightforward labelled list — for example, the Banshee (p. 23) is immune to a variety of damage types and conditions, and is resistant to another list of damage types. This works similarly to previous editions and won't require an adjustment in how you think about it.
Magic resistance, on the other hand, uses the special trait space to define how it works for that specific creature. An example is the Death Knight (p. 47), which has Magic Resistance — it says how it works for Death Knights as part of the creature:
The death knight has advantage on saving throws against spells and other magical effects.
This way of defining special traits with an ad hoc rule particular to that creature allows the designers and the DM significant flexibility when creating creatures. It also means that you won't find a general explanation of how magic resistance works outside of a creature's entry, because it's individual to each creature.
Although magic resistance works identically for most (all?) other creatures in the MM that have it, defining it per-creature in 5e means you can't rest comfortable knowing how a monster you're facing works: DMs have the power/authority to alter creatures' special traits, and new creatures (either new-to-your-PC, or in new books) can be made that have a "Magic Resistance" with a different definition.
A good example of this way of using special traits to define traits unique to one creature is the Rakshasa's magic immunity:
Limited Magic Immunity. The rakshasa is immune to spells of 6th level or lower unless it wishes to be affected. It has advantage on saving throws against all other spells and magical effects.
It specifies which spells it's immune to and when. You can probably see how the flexibility inherent in this design approach could be used to give a different creature a trait with the exact same "Limited Magic Immunity" name, but with a different description that makes it immune to only Illusion spells, or spells of 3rd level or lower, or spells cast by a cleric, etcetera.
Additionally, see how this gives a magic resistance effect identical to the Death Knight's Magic Resistance, but without the Rakshasa having a Magic Resistance trait! It's just part of the ad hoc definition of its Limited Magic Immunity trait.