Team Bonuses can boost the Health, Armor, Magic or Attack of your troops depending on which Team Bonus is active. Team Bonuses can be determined by having a certain number of unique troops of a certain Troop Type, Kingdom or Color. There are also Permanent Bonuses given by your Kingdom Levels and even some benefits your Guild can give. These bonuses are given to the entire team, even to troops that don't share 'type' or 'Kingdom' qualities receive benefits!
Kingdom Stat Bonuses are earned by Unlocking and leveling Kingdoms to 10. Once at 10, each Kingdom will give a permanent Skill bonus to ALL troops and your Hero. You can further improve the Skills that each Kingdom can give by earning Kingdom power and reaching 5 Stars for that Kingdom.
Find more information about Kingdom Stars here: What Do The Stars On My Kingdom Mean?
Guild Bonuses Are applied when you complete the final (12/12) task of each Colored Statues in your Guilds 'Tasks' screen. These bonuses are unlocked and will expire in 7 days unless the task is completed again in the NEXT week, in which case another 7 Days are added to the Guild Statue Bonuses expiration time.
Find more information about Guild Tasks here: Completing Basic And Legendary Guild Tasks
Note: All Guild tasks have been completed and these are the maximum bonuses you can receive for your team that are given from your Guild
Troop Type Bonus are given to teams that have three or four troops that share a type (two troops of the same type will NOT give this bonus). Each type has its own specific (but not unique) set of bonuses. Because troops can have two types each, it is possible to have multiple troop type bonuses on one team.
Kingdom Team Bonuses are given to teams that have two, three or four troops that share a kingdom - larger bonuses are given for having three or four troops. Each Kingdom has its own specific range of bonuses (although they are not all unique). It is entirely possible to have a team with two troops from one kingdom and the other two from a second kingdom, and get both of the kingdoms' minimum two-troop bonuses.
Color Bonus are given to teams that have all four troops sharing a color, i.e. four Yellow Troops (troops can be multicolored so long as they all share at least one color). View your 'Bonuses' screen to see what Color gives what benefits.