One aspect of the game that only comes into play in player-vs-player mode is that of elemental type advantages. While not as in depth as Pokemon's system, there is still a relationship of strengths and weaknesses between the eight types of Skylanders. When a type advantage is in play, extra damage is dealt just like when a Skylander is experiencing their advantage zone in the game's story mode. This is demonstrated in the game with an additional damage counter shown inside an icon of the attacker's type.
Here is a chart showing the relationships between the eight types. Each type has one strength and one weakness, leaving it neutral toward the other five types. Strengths are read clock-wise, such as "Water is strong against Fire, Fire is strong against Air." Weaknesses are read counter clock-wise, such as "Water is weak against Life, Life is weak against Undead."
Some other ways to remember the circle: you Fire at something in the Air, Air soars above Earth, Earth smashes your Technology, Technology beats Magic (think modern science vs the dark ages here), and Magic is probably your only weapon against the Undead. Unless they're Zombies, I suppose, in which case there are plenty of modern options.
Once you delve into the player-vs-player side of the game (which we love at our house), you will definitely need to know this information!