The speaker opens with apostrophe, addressing an unidentified subject directly. Right away, the speaker's love for this person becomes clear, since the speaker immediately focuses on the lover's heart. Of course, heart-related imagery often appears in love poems, but the speaker's thoughts about the lover's heart are somewhat unique. Using an anaphora to repeat the words "i carry," the speaker continues in the parentheses by suggesting that the lover's heart exists inside the speaker's own. Whereas the original idea of carrying the lover's heart isn't particularly notable, the image of a heart within another heart is somewhat strange and thus all the more meaningful. Indeed, that the lover's heart is inside the speaker's creates a sense of unity, as if these two people are so close that their most vital body parts are practically one.
Needless to say, the heart frequently functions in literature as a symbol for love, but it's worth considering the actual anatomical function of this bodily organ. Because the heart is responsible for pumping blood through the body, it is perhaps the most important organ. As such, the fact that the lover's heart is inside the speaker's suggests that the lover is integral to the speaker's very existence, effectively becoming the speaker's life force.
No matter how close these two people are, though, it's obvious that this image of a heart existing inside another heart is a metaphor. After all, the lover's heart isn't literally inside the speaker's—rather, this is simply a way for the speaker to express just how close and dear these two people are.
Similarly, the strange use of punctuation in the first line reinforces the idea that the speaker and the lover are inseparable, as if putting a space between the end of the first phrase and the opening parenthesis ("me(carry") would be too painful for the speaker. In other words, the lack of white space between "me" and "(carry" softens the effect of the caesura that would otherwise occur between the two phrases, and this only underlines the feeling of closeness between the speaker and the lover. In this regard, E. E. Cummings's characteristically odd syntactical style helps the speaker more thoroughly communicate the feeling of unity between the speaker and the lover.