I've started a new round and will be heavy on magicka and illusion, alteration, and destruction. Not sure about conjuration -- I don't quite get what it does. Early on I picked up the Fury spell and it's very funny: two or three bandits come charging at me so I fling a Fury at one of them and watch him or her attack the others! But I see that it's only up to level 6? What can I get after that that will do the same thing -- and where do I get it?

It looks like 'Frenzy' is the next step up: http://elderscrolls.wikia.com/wiki/Illusion_(Skyrim)

Frenzy is the adept version of the spell and mayhem is the 2 handed master version.

Looks good. Thanks a lot.

On the other hand, Fury can work all the way up if you have the augmenting perks like Kindred mage and Rage plus dual casting. At lowish levels, like 40 Illusion, you can have Kindred mage and dual for effectiveness up to level 34 enemies with Fury.

What conjuration does, is allow you to summon helpers that can help you in a battle. There are several of them, plus there are weapons you can summon to use. If you use an atronach, just make sure you use the same element. If you conjure / summon a frost atronach, use frost. If you summon a fire antronach, use fire. Otherwise you can damage the health of the atronach you summon by using the wrong element. Hope that helps.

Raising the dead to fight for you, summoning minions from the planes of Oblivion to fight for you, conjuring weightless arcane weapons to use. Doesn't get any cooler than conjuration in my opinion.