A Buff is an enchantment or other special condition that is currently active on a unit. Buffs can be positive (e.g. gain strength) or negative (e.g. unable to move). For each Buff, you can see its effect, how long it will last (unless it is permanent), and its caster. Clicking on the caster's icon next to a Buff will take you to the caster of that Buff, if they are still alive. All Buffs are created by a special ability, except for Combat Experience and Fortifications.
Each time a unit wins a battle, it gains Combat Experience. Combat Experience grants each individual in a unit +1 Strength for each combat victory.
When merging units, ensure you select the unit with the buffs you want to keep, and merge other units into that unit. All units merged into the selected unit will gain that unit's buffs. This also works for negative buffs that you want to remove, or special abilities that you want to use.