The "glimpses" that the poem refers to are shown to be dazzling and beautiful glimpses of nature that truly point us towards the intense and inspirational beauties of the natural world that our mind seems to find so difficult to comprehend. The speaker uses the example of being on a train and looking out of the window and suddenly seeing some flowers before they vanish as the train moves on. He finds it difficult to identify them, and ends up by asking the rhetorical question:
Was something brushed across my mind
That no one on earth will ever find?
The speaker suggests therefore that the "glimpses" that the poem refers to come from "Heaven" and that they are only given to those "Not in a position to look too close." The glimpses are therefore snatches of heaven or of a purity so intense and beautiful that we as humans are only able to see them as glimpses. The implication of the poem is that we are unable to comprehend the realities of heaven and thus are only able to see such realities in "snatches" or "glimpses" in our busy lives.