As for what is Necrotic damage:
Necrotic damage, dealt by certain undead and a spell such as chill touch, withers matter and even the soul. (PHB, p. 196).
You can think of it as damage the corrupts flesh, matter, and even impacts the very soul of a creature. My suggestion would be to describe it as a quick acting rotting effect with the flesh blackening and withering along with a feeling akin to a strong sense of sadness or loss.
The different damage types interact with various attacks and defenses. A creature may be vulnerable to necrotic, resistant, immune, or have nothing special in regards to this type of damage.
Like the other types of damage, it comes into play as the rules specifics says it comes into play.
If you look on page 197 of the PHB, first column there is a general note on Healing. There is no mention of any special treatment of necrotic damage over any other type of damage, nor do any of the healing spells mention necrotic damage.
Specific abilities and spells can deal both necrotic damage and effect healing. However it is not a function of necrotic damage but the ability/spell itself. It will be stated specifically in the description what the effect will be. For example Chill Touch on page 221 states
On a hit, the target takes 1d8 necrotic damage, and it can’t regain hit points until the start of your next turn. Until then, the hand clings to the target.
while Circle of Death on the same page says
Each creature in that area must make a Constitution saving throw. A target takes 8d6 necrotic damage on a failed save, or half as much damage on a successful one.
Both deal necrotic damage but only Chill Touch has any impact on healing. Circle of Death just deals the damage.
Another example is the Vampire Bite in the Monster Manual (Vampire)
Bite (Bat or Vampire Form Only). Melee Weapon Attack: +9 to hit, reach 5 ft., one willing creature, or a creature that is grapp led by the vampire, incapacitated, or restrained. Hit: 7 (1d6 + 4) piercing damage plus 10 (3d6) necrotic damage. The target's hit point maximum is reduced by an amount equal to the necrotic damage taken, and the vampire regains hit points equal to that amount. The reduction lasts until the target finishes a long rest. The target dies if this effect reduces its hit point maximum to 0. A humanoid slain in this way and then buried in the ground rises the following night as a vampire spawn under the vampire's control.
You will note that its ability to reduce a target's hit point maximum is spelled out in the attack's description. This is because the necrotic keyword is not sufficient to cause this effect. Instead it spells out how the attack does damage and reduces the hit point maximum, as well as how it is recovered from and what happens when HP goes to zero.
Unless this text or something similar to it is present in the description of the power, ability, or spell then necrotic damage is healed like any other damage.
The inability to heal this damage is contingent on the key word hit point maximum. You cannot heal beyond the maximum hit points. The decrease can only be countered by the method outlined in the text or a spell the effects maximum hit points like Greater Restoration.