The significance of Hezekiah's spreading the letter before the Lord is that it is his way of revealing his total dependancy for help in a tangible way; this letter is an affront to the living God; nothing Hezekiah can do but give it over to the Lord.
The significance for us is to learn to do the same thing: hand our troubles, problems, challenges to the Lord and then follow his direction; seek his will and follow through with action. We have this need to be in control; feel out of control, especially if we have said "yes" to what seems like too many requests for help, yet if these are activities that God would have us do, then He will be there with us and give us the strength & energy to do His Will. He will also provide the financial resources to provide for our needs when we are generous with others who have needs that we are aware of.