What effect does increasing the magic skills have?

For all the magic schools, the skill description only mentions that the skill makes it easier to cast those spells. You also need a certain amount of skill to get the perks associated with that skill.

Aside from unlocking perks, what effects does increasing your skill in Destruction, Alteration, Conjuration, Illusion and Restoration have? Does it increase the damage of destruction spells, for example?

Making it "easier to cast" is relatively straightforward - it reduces the Magicka cost of the spell, meaning you can cast them more often.

This is similar to how things worked in Oblivion. (I'd link you to the UESP page documenting this, but the Site's still getting hit pretty hard from all the Skyrim traffic)

Each spell has a "base cost", which is modified by the following formula:

spell cost = base cost * skill multiplier * perk multiplier * equipment multiplier * dual cast multiplier
skill multiplier = 1 - (skill/400) ^ 0.65

This means that at 100 skill, spells cost 60% of the base cast (further modified by perks and equipment).

This isn't combat related, but as Affe has pointed out below, increasing your magic skills is required to buy high-end spells from vendors.

What he means by 1% per skill is.

the first skill point gives you a 1% decrease.

so 99% cost

the second one gives you a 1% of the 99% cost, so in truth it decreases by 0.99%

so 98.001 cost

then -0.98001

And so on

at level 100 you will have a cumulative 50% reduction