Most characters have some special ability that they can use as listed in their effect text. The numbers in these colored boxes are how many dice the character rolls of that color. Troops are like characters, but they represent large amounts of secondary characters in the game and they usually only have a Combat Ability. Troops and characters usually participate in challenges, but do not interact with one another directly. Instead, characters interact with characters and troops interact with troops.
Fleets represent the primary military capability of any race.
An individual faction can only have one copy of any give fleet out at a time. Some fleets can only be played if your faction is from a particular race. Groups represent large numbers of minor characters or some organization. Some group cards can only be played if you are playing a specific race. Most group cards don't have abilities like characters, but have effects on the gameplay when you use them.