The speaker is the "Old Man" of the title, and he's in a reflective mood. He begins by describing a picture he used to see "before [his] eyes," though the rest of the poem makes clear that this image is really in his mind (he's not talking about a physical painting).
Line 1 uses enjambment to create a brief moment of tension, which leaves the reader to guess what's coming next. Line 2 reveals that the speaker used to see "A picture painted, like the rainbow, bright." Decorative alliteration helps evoke the beauty of the picture; those, punchy plosive /p/s also hint at the picture's powerful impact on the speaker's life.
The speaker compares this picture—which he never describes in detail—to "the rainbow, bright." His simile suggests that the picture was beautiful and awe-inspiring, but also a kind of illusion. Rainbows exist only as a trick of the light; they might look solid, but one can never get close to them and touch them. Already, then, the poem hints that this isn't a real picture but a symbolic vision, reflecting some fundamental promise and/or disappointment related to life itself.
Indeed, this picture only ever appeared "far, far off in th'unapproachable distance." The emphatic epizeuxis of "far, far" makes this distance seem all the more "unapproachable." If the reader is wondering, by now, what the picture means—well, that's kind of the point. As a child, the speaker felt a deep-rooted longing for something, but he didn't know then (and doesn't know now) precisely what it was. The juxtaposition established by the title is important here: this is an "Old Man" reflecting on his time as a kid, when the world seemed new and beautiful. Perhaps, back then, he felt instinctively optimistic that his future life would turn out as he hoped. Or maybe this far-off "picture" held out the promise that the confusion of childhood would someday resolve into certainty. In any case, he yearned for something that wasn't yet his.
These opening lines also establish the poem's form. "Old Man" is written in iambic pentameter, meaning that most of its lines contain five metrical feet following an unstressed-STRESSED pattern (da-DUM). Listen to lines 1-2, for example:
At six | years old | I had | before | mine eyes
A pic-| ture paint-| ed, like | the rain-| bow, bright,
This steady, measured rhythm seems appropriate for someone speaking from long experience, reflecting soberly on the idealism of his younger days.