I could not bring My passions from a common spring (3-4)
"Spring" here refers to a natural body of water. The connection between nature and human passions is something the poem develops later, especially when the speaker talks about the "mystery" he can access via mountains and fountains and torrents.
Then- in my childhood, in the dawn Of a most stormy life- was drawn (9-10)
The rhyme on "dawn" and "drawn" is totally cool here. Dawn makes us think of new beginnings, and we know "drawn" goes with mystery. In a way, then, the mystery that the speaker is about to describe is like the sunshine that shows up later. It's the beginning of a new era.
From the sun that round me rolled In its autumn tint of gold, (15-16)
Sun and gold—those are pretty positive things. Gold makes us think of money and riches, whereas we associate the sun with warmth and life. The natural world here seems like a comforting, nurturing presence that enwraps the speaker.
From the lightning in the sky As it passed me flying by, From the thunder and the storm, (17-19)
The long "I" sound in "lightning," "sky," and "flying" is telling. It reminds us of all the times the speaker says "I" and implies that there is a close connection between the speaker and the natural world. They're totally BFFs.
And the cloud that took the form (When the rest of Heaven was blue) Of a demon in my view. (20-22)
This lone demon-cloud is kind of like nature's version of the speaker. The cloud is completely different when compared to the "blue" sky, just as the speaker is totally different when compared to all his peers.