What does the term 'Spot Healing' mean in World of Warcraft?
"Spot healing" just means healing whoever needs healing at the time. Typically healers have a specific assignment such as tank healing or raid healing, in order to prevent overlap and to make sure that everyone who needs healing can get it. Spot healing can refer to a raid healer who puts some heals on the tank during an emergency, or who uses a single target spell to give a bit of extra healing when they would normally be using AoE heals on multiple targets. Basically, spot healing is anything that falls out of your normal expected healing rotation due to some extra unintended damage or some other reason. Someone might even be assigned to be a spot healer and their job would be to heal whoever needs healing the most at any given time. The reason you wouldn't want everyone healing this way is because if one target needed healing and every healer tried to heal them at the same time, that player is going to get way more heals than they need while everyone else gets no healing and the situation can become even worse.
Concise description
"Spot healing" is the short form of "On-the-spot healing", it means healing a target for large amounts that unexpectedly / exceptionally needs a large burst of heal, requiring the healer to make an "on the spot" decision to heal this target with a strong heal, as opposed to just doing their normal spell rotation to keep the group/raid healthy. It can also mean that hybrid or damage-dealing classes with heal spells make this same "on the spot" decision to use them to save a fellow raid member.
Elaboration
Healers in WoW have a usual range of spells they use to keep everyone at good levels of health. They usually choose these spells to be as mana efficient as possible, since mana is again an important resource in WoW.
Sometimes though, one or a few players take more damage than can be healed with the "usual" rotation. As an example, Druids heal mostly with healing over time effects (hots) - Rejuvenation, Lifebloom & Wild Growth. Such effects are cheap to cast, but they only heal small amounts quickly and provide more value over longer time. If one player of the group suddenly drops to low health and is in need of a large burst of heal immediately, he is then "spot healed" with a large single-target heal that swiftly brings him back to reasonable health levels - in case of Druids, this would be Swiftmend or Regrowth.
Spot healing just refers to healing players that take excessive damage and are in need of a large burst of heal to bring them back to reasonable health levels. This damage can either occur due to mistakes (standing in an avoidable mechanic) or due to boss mechanics that target a single player - e.g. a strong "damage-over-time" (dot) effect that is randomly cast on one or few people and can't be dispelled (removed from the player).
Some classes are better at spot healing then others due to the available healing spells. The aforementioned druids are exceptionally bad at spot healing, it costs them a lot of mana compared to the heal it generates, while other classes are better suited to it.
Good healers in a raid will form an understanding who will spot heal more and who doesn't. It is desirable to avoid overlap in spot healing. Two healers spot healing the same target usually results in a large amount of overheal - wasting heal and mana, or at worst results in deaths (multiple players taking lots of damage, healers all healing one target instead of each healing one player).
Note that tanks are an exception to this rule. Tanks constantly take lots of damage and typically need to get spammed with strong single-target heal spells. This is not "spot healing", since its not an "on the spot" decision to heal the tank (its not unexpected), but rather part of the normal gameplay. Healing a tank is usually simply referred to as "tank healing". That doesn't mean that tanks never get spot healed, tho. There is certainly some overlap, and tank healing can at times be spot healing if required.
Note that "single target healing" is not the same as spot healing - there is a large amount of overlap, but they are not the same. Putting a hot on single player is single-target healing, but it is not considered spot healing. Spot healing is (usually) single target healing, but not the other way around.
It means "single-target healing" as opposed to AOE healing. Typically used when one ally is much lower health and needs help more that the whole team. It's a term used in other games but mostly popular in MMO's like WoW, in FPS's I've heard it more often called a "pocket healer". Slightly more info here on the WoW forum.