The Iron Hills, the most powerful kingdom in Wilderland?

[Boromir88]

King Dain (and his people) were always a staunch resistor to Sauron. The dwarves (and Men of Dale) role during the War of the Ring must not be overlooked. The main focus is on Gondor...that is the place Sauron hates the most and feels it would be the toughest to take over. So, it is Gondor that would bare the bulk of Sauron's focus and attack. However, eventhough if that's the focus of the story we are told about in the Return of the King; I don't think the resistance of Dain's people should be cast aside.

While Sauron was attacking Gondor he also sent another force to attack the Dwarves of the Iron Hills, and it is them that hold off and stop Sauron's advance to Rivendell and beyond.

Sauron had a brilliant strategy...he made some mistakes executing his plans; but his plan was brilliant. He wanted to prevent another Last Alliance like he faced in the 2nd Age. Eventhough if the Free Peoples would not be able to put up the numbers like they did in the Last Alliance, nevertheless Sauron wanted to prevent them all from uniting together again. So, what he does is he feels Gondor is his main threat, and he prevents other possible allies from helping Gondor out. Gondor would take the brunt of Sauron's assault, but to prevent 'outside help' Sauron effectively ties up the other areas. He gets Saruman on his side to attack Rohan...probably Gondor's greatest ally. He sends a force to attack the Dwarves and tie them up...hoping to continue on into Rivendell and beyond. He ties up the Elves of Lorien and of Mirkwood with attacks from Moria and Dol Guldur respectively. What Sauron plans is brilliant; he doesn't do the best job executing his plan, but the plan itself is an excellent idea.

So, now comes the importance of the Iron Hills...which I think is evident in the quote you provided; and what A_Brandybuck talks about. I think it's a tribute to teh strength of the dwarves that Sauron didn't want to fight them unless he had to...remember at first he sent messengers to Dain to try and win him over and avoid fighting them:

'Then about a year ago a messenger came to Dain, but not from Moria - from Mordor: a horseman in the night, who called Dain to his gate. The Lord Sauron the Great, so he said, wished for our friendship...
'As a small token only of your friendship Sauron asks this,' he said: 'that you should find this thief,' such was his word, 'and get from him, willing or no, a little ring, the least of rings, that once he stole. It is but a trifle that Sauron fancies, and an earnest of your good will. Find it, and three rings that the Dwarf-sires possessed of old shall be returned to you, and the realm of Moria shall be yours for ever. Find only news of the thief, whether he lives and where, and you shall have great reward and lasting friendship from the Lord. Refuse, and things will not seem so well.'~The Council of Elrond

This should speak to the strength of the Dwaves...Sauron didn't want to deal with them! He tried to offer them terms of a 'peace' so he didn't have to fight with another place in order to achieve what he wanted. However, the Dwarves saw through into Sauron's purposes and rejected the offer:

'Heavy have the hearts of our chieftains been since that night. We needed not the fell voice of the messenger to warn us that his words held both menace and deceit; for we knew already that the power that has re-entered Mordor has not changed, and ever it betrayed us of old.~ibid

What the Dwarves did was quite important. Even though if it's not the focus on the War of the Ring they held of Sauron's advance further west to Rivendell and Eriador. They indeed were the staunch defenders of the North. As A_Brandybuck mentions, Mirkwood may have been some help; but I think we must not forget they were having troubles of their own fighting off the assaults from Dol Guldur...and needed help from Lorien to end the problem.

What the Dwarves and Men in the area did first rejecting Sauron's offer of peace (since they knew Sauron was going to deceive them), and second holding off his advance further is quite a testament to the strength of the people in the area to resist Sauron. If Sauron trying to offer them a peace so he could avoid confrontation with them isn't already enough.