What does the light symbolize, how does Scrooge try to "extinguish" it, and does he succeed?
The light came from the head of the Ghost of Christmas Past:
But the strangest thing about it was, that from the crown of its head there sprung a bright clear jet of light, by which all this was visible; and which was doubtless the occasion of its using, in its duller moments, a great extinguisher for a cap, which it now held under its arm.
For some reason, the light began to upset Scrooge and he asked the spirit to cover his head.
"What!" exclaimed the Ghost, "Would you so soon put out, with worldly hands, the light I give? Is it not enough that you are one of those whose passions made this cap, and force me through whole trains of years to wear it low upon my brow!"
Scrooge reverently disclaimed all intention to offend or any knowledge of having willfully bonneted the Spirit at any period of his life. He then made bold to inquire what business brought him there.
The spirit is saying that his head should never be covered. It is the light of the spirit of Christmas, and he says that the it is the passions (or perhaps negative attitudes) of people like Scrooge who created the hat in the first place.
Near the end of Stave Two, Scrooge is very upset because the ghost has shown him his past love and the way that her life turned out and the way that she and her family pitied him. He became overwhelmed and begged the spirit to take him back. As he was begging, he saw that the light was “burning high and bright.” He fought to cover the light.
In the struggle, if that can be called a struggle in which the Ghost with no visible resistance on its own part was undisturbed by any effort of its adversary, Scrooge observed that its light was burning high and bright; and dimly connecting that with its influence over him, he seized the extinguisher-cap, and by a sudden action pressed it down upon its head.
The Spirit dropped beneath it, so that the extinguisher covered its whole form; but though Scrooge pressed it down with all his force, he could not hide the light, which streamed from under it, in an unbroken flood upon the ground.
He was conscious of being exhausted, and overcome by an irresistible drowsiness; and, further, of being in his own bedroom. He gave the cap a parting squeeze, in which his hand relaxed; and had barely time to reel to bed, before he sank into a heavy sleep.