I'm wondering what the differences between Shield, Shock Shield, Fire Shield, and Frost Shield are. I know exactly what Shield does but I'm unsure of what the Elemental Shield spells do. Can somebody please explain this to me?

Elemental shields do two things actually. They defend against either fire, frost or shock in addition to damage against blows, i.e your armor rating improves

So they are much better than normal shields. Interesting.

They can be useful if you know you'll be encountering a particular type of enemy, for example fire shield when going into oblivion.

Assuming Skyrim implements them the same as oblivion and morrowind, they will - as mentioned above - add to armor rating and resist the element. So given the same magnitude, it's better than non-elemental shields. However they are usually more expense to cast or harder to make in potions. But oddly not so much with enchanting.

The theory is that they surround the character with a wall of that element. So a Shock shield would surround the character with "electricity" which respell melee attacks. But a shock spell trying to get through will also be partially "absorbed" or "counteracted" by the electric shield.

Visually this shows up better in Morrowind where where you see an effect from the shield.

Exactly. But being better, the elemental shields are more expensive magical effects to use as Savlian mentions - and worth it. Many consider the +17 level transcendent sigil stones for those effects to be extremely useful.