I was wondering what it means when a character has a bar across thier defensive shield icon on thier powers card.

Not everyone has it. could someone give me a clarification?

That power is called Indomitable. It means the character doesn't take pushing damage. It still, however, can only take one action per turn.

An easy way to explain it is permanent Willpower.

Except technically this is not perma-Willpower. There are Feats that ignore Willpower, sush as Nova Blast, however since Indomitable just ignores pushing damage, it's not technically Willpower.

It's not really permanent either. All abilities except team abilities can be Outwitted, in which case the figure would take pushing damage as usual. Also, should the Indomitable figure gain Earthbound by some means (say if Ms Marvel gets in range of the Aerial Baffler), it will also cause it to gain the normal shield icon and lose Indomitable.

Sorry to resurrect this, but one additional questions please:

Can you turn off 'Indomitable', just as you can turn off Willpower?

(The power description doesn't say 'Non-optional', so I'd assume the answer was "yes".)

From what I know, it's not a Power, so you can't turn it off. Like with the Giant symbol - if you have it, you have it - only if you gain it by a Power, you can cancel it, just like you can cancel any power unless it says "non-optional".

This is incorrect.

You cannot cancel the SYMBOL, but the ability granted by the symbol, INDOMITABLE, is able to be canceled.

And so I learn something new! Thanks for the info!