Intensified spell says:
an intensified spell increases the maximum number of damage dice by 5 levels.
What does it mean that it improves damage dice by 5 levels? That spells of damage based on the caster level is affected? For example, a Fireball deals 1d6 points of fire damage per caster level, if I'm level 4 and I'm casting fireball, it deals 9d6 instead of 4d6?
Intensified Spell does not improve the damage of a spell per se, but increases the damage cap. Let's look at fireball (emphasis mine):
A fireball spell generates a searing explosion of flame that detonates with a low roar and deals 1d6 points of fire damage per caster level (maximum 10d6) to every creature within the area.
Damage is based on your caster level, but it does not increase after CL 10, because of the cap in the spell description. This cap, i.e. the "maximum number of damage dice", is modified for an intensified fireball:
A fireball spell generates a searing explosion of flame that detonates with a low roar and deals 1d6 points of fire damage per caster level (maximum 15d6) to every creature within the area.
Note that a CL 10 fireball and a CL 10 intensified fireball deal the same amount of damage, but starting at CL 11, an intensified fireball's damage is higher than a regular one's.
an intensified spell increases the maximum number of damage dice by 5 levels.
The Intensified Spell feat will allow you to increase this spell by 5 steps higher then the standard maximum level.
For example: Fireball reads:
A fireball spell generates a searing explosion of flame that detonates with a low roar and deals 1d6 points of fire damage per caster level (maximum 10d6)
An Intensified Fireball will increase the maximum damage to 15d6 at level 15. Casting this spell at level 4 will still give you 4d6.
If you wanted to look at increasing the damage done at lower levels, I would suggest looking at the Empower and Maximize Spell feats to increase the total damage.
It means that if the damage cap on a spell was normally 10d6 at Caster Level 10, it would increase the maximum damage die by 5 at Caster Level 15. Therefore changing the spell to be up to 15d6 instead of the normal 10d6.
