Intensify just raises the limit, nothing more.
CL 3, normal: 3d6
CL 3, intensified: 3d6
CL 8, normal: 5d6
CL 8, intensified: 8d6
CL 13, normal: 5d6
CL 13, intensified: 10d6
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Normally, a level 8 caster does 5d6 damage with shocking grasp, because the maximum is 5d6.
With Intensify Spell, the maximum is (5+5)d6 or 10d6. A level 8 caster is not high enough level to do 10d6. A level 8 caster would do 8d6 damage, 1d6 per caster level.
A level 12 caster with Intensify Spell does 10d6 damage, because Intensify Spell makes 10d6 the maximum damage.
"You must actually have sufficient caster levels to surpass the maximum in order to benefit from this feat" means that a level 4 caster gets no benefit from the feat. A level 4 caster does 4d6 damage with or without the feat.
When you have a caster level higher than 5, by default shocking grasp does 5d6 points of damage and no more than that.
If level 8 and using Intensified Spell metamagic feat on shocking grasp, then you do 8d6.
Benefit: An intensified spell increases the maximum number of damage dice by 5 levels. You must actually have sufficient caster levels to surpass the maximum in order to benefit from this feat. No other variables of the spell are affected, and spells that inflict damage that is not modified by caster level are not affected by this feat. An intensified spell uses up a spell slot one level higher than the spell's actual level.
Intensified Spell simply raises the maximum number of damage dice for a spell by 5 levels, in shocking grasp's case its new maximum damage is 10d6 (5d6 normally + 5d6 intensified) at caster level 10. But the second sentence says you actually need the sufficient caster levels over the spell's maximum if you want to benefit. NOT simply adding another 5d6 to the shocking grasp's damage.
So your example of level 8 character only has 3 levels over the maximum of 5d6 (5 caster levels of 1d6 for shocking grasp), so the intensified shocking grasp is 8d6 for caster level 8.