In AFK Arena, each faction is strong against one particular faction and weak against another one. This means that characters can do up to 25% more damage in a fight with another characer from the faction they are strong against.
For example, Lucius who is a Lightbearer will do up to 25% more damage against Brutus who is a Mauler. Lucius will, however, take up to 25% more damage from Shemira who is a Graveborn.
AFK Arena also has a team faction bonus that gives your entire team a percentage boost to HP and Attack based on how many characters of a certain faction are in battle. For example, you can get a 15% ATK and 20% HP boost if your team has 4 Lightbeares heroes. Here is the chart where you can find more detailed information on team faction bonuses.
However, one thing to keep in mind is that sometimes a good and balanced team comp is way more important than the team bonuses. This is specially true on the later stages of the game.