Having an aura active will provide you with the listed benefits. Fully upgraded fire is 15%speed and attack, +30 dmg. Ice is -7% speed -15% attack and 9mps. The stacks you are referring to are the aura's you get when you switch forms, you get +70 damage for 15 seconds when you switch from fire to ice, no matter what skills you take. When switching from ice to fire you gain an amount of mana regen.
The stacking of 5 X aura's is the result of 5 TB being present on your team with the same level aura activated.