What exactly are, 'supported skills'?

I am new to POE in general and am confused about something. If I equip a support gem for, say a skill that uses cold damage inherently, but the support gem says something like: "40% more cold damage and 20% less fire/lightning damage for supported skills" What is the 'supported skill' in this case? If the skill is a cold damage skill, why does the support gem mention less other damage for supported skills?

What exactly does the supported skill even refer to?

It means it applies this effect to any Skill Gem that the Support Gem is qualified to support (as long as it's linked, of course).


All gems typically have Tags in the top area of their description, such as... Spell, AoE, Cold, Projectile, and all sorts of other possibilities. A lot of the time, these tags can help you identify if the Skill can be supported by the Support. (The Support Gem will also have, in its description, maybe a list of things it CANNOT support, or maybe a list of things it DOES support. Like it might start off by saying, "Supports an attack," which lets you know it does not support a SPELL.)




When a Support Gem says "supported skill," it is referring to any applicable Skill Gem(s) it is linked to! I hope this answers your question fully.




Edit:
Also, all that being said... It sounds like you're referring to a Support Gem that probably has the "Prismatic" tag, or mentions Prismatic somewhere? If that's the case, then I believe that gem only supports Skill Gems that have the Prismatic tag (up where you would see other tags, too, like Spell, AoE, Cold, Projectile, etc etc).


Edit 2:
Another easy trick to know if the Support Gem is successfully supporting your Skill Gem is to see if the mana cost changes when you apply the Support Gem to the socket.

Since the question seems based around a PoE2 support gem rather than PoE1...

Typically, a Support Gem will only affect the skill that it is socketed into.
If you have Spark and Frostbolt in your build, and you add the support you mentioned to Frostbolt, the damage of Spark will be unaffected.


With Triggers, though, it's possible for a Support Gem to be supporting more than one skill.
If Spark and Frostbolt weren't in different skill slots, but were instead socketed in a "Cast on Shock" gem together with the support you mentioned--both skills would be affected by it.


As for "why the support gem mentions less other damage of supported skills", that is because skills are not limited to the base damage type of the skill.
Even though Spark does Lightning damage and Frostbolt does Cold damage normally, if you allocate Avatar of Fire, you would end up dealing Fire damage with both skills. There are a variety of other ways to add damage of other elements to a skill.

Woops! Wrong forum section. Thanks!