It's hard to know what it means from the King James. It's 500 years old. You can also look at a longer part of that passage.

(Romans 8:19-28 NIV) The creation waits in eager expectation for the sons of God to be revealed. {20} For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope {21} that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God. {22} We know that the whole creation has been groaning as in the pains of childbirth right up to the present time. {23} Not only so, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for our adoption as sons, the redemption of our bodies. {24} For in this hope we were saved. But hope that is seen is no hope at all. Who hopes for what he already has? {25} But if we hope for what we do not yet have, we wait for it patiently. {26} In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express. {27} And he who searches our hearts knows the mind of the Spirit, because the Spirit intercedes for the saints in accordance with God's will. {28} And we know that in all things God works for the good of those who love him, who have been called according to his purpose.

I don't agree with this:

"There are destinies hanging on your shoulders that are depending absolutely on you. If you don't succeed, they won't succeed. If you don't make it, they won't make it."

No, I'm not responsible for anyone else's salvation except my own. Sure, it's my job to share the gospel with those who are willing to listen. I need to be a good example of my faith at all times. But everyone's salvation is their own responsibility.

In Isaiah 60 it's obviously God talking to Israel:

(Isaiah 60:1-7 NIV) "Arise, shine, for your light has come, and the glory of the LORD rises upon you. {2} See, darkness covers the earth and thick darkness is over the peoples, but the LORD rises upon you and his glory appears over you. {3} Nations will come to your light, and kings to the brightness of your dawn. {4} "Lift up your eyes and look about you: All assemble and come to you; your sons come from afar, and your daughters are carried on the arm. {5} Then you will look and be radiant, your heart will throb and swell with joy; the wealth on the seas will be brought to you, to you the riches of the nations will come. {6} Herds of camels will cover your land, young camels of Midian and Ephah. And all from Sheba will come, bearing gold and incense and proclaiming the praise of the LORD. {7} All Kedar's flocks will be gathered to you, the rams of Nebaioth will serve you; they will be accepted as offerings on my altar, and I will adorn my glorious temple.