The speaker of the poem is an older man sitting with the corpse of Evelyn Hope, a 16-year-old girl who has recently died. He is "thrice her age" (line 21). Even though she "had scarcely heard [his] name" (line 9), he longed for her. She was too young to have yet loved, so he never made any direct proposal and wonders whether it is now too late.
He spends much of his address praising her purity and reflecting on how their relationship as "fellow mortals" (line 24) might have made them partners under other circumstances. He assures himself that their union is not forever prohibited and believes God has merely delayed it until they meet again and he can have her.
When they rejoin, he will tell her of the many phases of life he has passed since this moment, but will also assure her that she has always been missing from his happiness. He promises to her corpse that he will always love her. He then places a leaf into her "sweet cold hand" as a secret that she will see when she reawakens with God and which will communicate to her his promise.
Despite the profuseness of the speaker's passion in this poem, he is easily categorized as disgustingly creepy. One gets the sense that Browning, in this poem published in 1855, wanted to explore the type of unfettered control fantasy that characterizes the Duke in "My Last Duchess," but without the sophistication in language, the charm, or the dramatic irony that pulls us into the earlier poem. Though a dramatic monologue, this poem lacks dramatic stakes - one gets the sense that the speaker is not worried about being interrupted during his long wail to the corpse, which could suggest he is a powerful man, and so he is able to expound on his feelings.
The most immediate grotesqueness of the situation is its physical circumstances. The speaker has obviously lusted after this girl from afar, without having ever made an effort to introduce himself. He acknowledges that she is too young to have yet loved, but this did not deter him from having developed an attraction deep enough that he believes they are fated to meet again in the afterlife. Again, the fact that she might have "scarcely heard his name," and yet he is given the opportunity to sit for an hour with her corpse suggests that he might be a man of renown who had picked out this young girl as a future conquest.
What is perhaps creepiest about the poem, however, is his insistence on expressing his feelings in such a pronounced pure form. He does not acknowledge the inappropriateness of such an attraction, but instead assumes that her nature of "spirit, fire and dew" (line 20) has made her an appropriate match for him. When he places the leaf in her hand at the poem's end, he means it to be a symbol of something pure and perfect, entirely unaware that he is crossing lines of propriety. The dramatic irony here does not draw us in as the duke's charismatic use of language does in "My Last Duchess", but instead horrifies us more, since this speaker is doubly unaware of how grossly inappropriate his actions and long-gestating affections are.
In the end, the poem is mostly concerned with the psychology of self-delusion. As noted above, the speaker is unaware of the extent of his delusion, so that the further he goes in assuming that he and the girl are fated to be reunited, the more we see his lack of connection with reality. His insistence on understanding their relationship (or lack thereof) in terms of godliness and purity only shields what we can assume is a much baser sexual lust. Of course, he'll never realize this but instead will spend the rest of his life considering himself a martyr for having lost this young girl, which makes the point that despite its title, this poem is not about Evelyn Hope at all but instead about a powerful man's level of delusions and grotesque perversions.