The LightCore Skylanders were first introduced in Skylanders Giants. There were 8 LightCore figures (one for each element).
Each of the LightCore figures are a reposed version of a Series 1 or Series 2 Skylander in Giants. So just looking at them (outside of the packaging) it could be difficult to tell which is which until you put them on the Portal.
In any case, you'll want to put them on the Portal sooner or later because that's when the real magic happens.
The LightCore Skylanders have a few LED bulbs in them. When you place the figure on the Portal, the LEDs in the figure will light up.
How does this work?
I'm not really sure about the technical side of it. All I know is that the figures light up and there are no batteries involved. I like to think it's magic!
In addition to looking cool, the LightCore Skylanders have another special ability.
When you place a LightCore Skylander on the Portal it will immediately perform an attack that defeats every enemy on the screen. This is particularly useful during large battles with large waves of enemies.
In Skylanders SWAP Force, the LightCore Skylanders made a second appearance. In SWAP Force there are also 8 LightCore figures.
These figures function in the exact same way as the original LightCore Skylanders.
There wasn't a lot of excitement surrounding the new LightCore figures with the exception of Warnado and Wham-Shell. These two characters were part of the Forgotten 8 (the eight characters from Spyro's Adventure that did not receive a Series 2 figure for Giants). Anyone who got into Skylanders after Spyro's Adventure had a hard time finding most of the Forgetten 8, so this was the perfect opportunity to add them to their collection.
The LightCore Skylanders were a novel idea, but with a price tag $2-3 higher than their standard counterparts a lot of fans did not buy into it.
The last LightCore Skylanders came with SWAP Force in 2013. All your LightCore figures still work in newer games, but it does not look like we will be seeing another round of LightCore figures any time soon.
As mentioned above, the first LightCore Skylanders came alongside the Giants. At that time, this was a fun, new technology that they really wanted to showcase.
So not only did the LightCore figures light up, but each of the Giants did as well.
However, the Giants do not have the LightCore prefix attached to their name and they do not have a special attack when placed on the Portal. For these reasons the Giants are not considered or referred to as LightCore figures.