There are two parts to your Strength Bonus that you see at the very bottom of your Battle Reports.
This Strength Bonus is a modifier that helps boost your attack or defence in PVP and PVE Battles!
What is the Ally Bonus?
The Ally Bonus is determined by how many Allies you have hired, and the individual bonuses they provide you for each type of Biome/Land.
Different Allies will provide different levels of bonuses, based on how they play their account. So making sure you optimize for allies that boost the type of land your Great Hall is located on is a winning strategy!
What is the Students Bonus?
The Student Bonus is based on the Heroes you are attacking with, or the Heroes you are defending with, and Heroes that offer passive abilities.
Different Hero abilities will provide bonuses to your strength based on a number of factors, like what Biome you are attacking or defending on, what other Heroes you are attacking or defending against, and the Rank of your Heroes because Rank boosts their unique Abilities!
Some Heroes have passive Abilities, meaning that their Ability will apply whether they are on your wall, in your march, or not equipped! This means its always beneficial to upgrade these Heroes even if they aren't the strongest one in your march!