In Emily Bronte's Wuthering Heights, the theme of love is treated from a metaphysical perspective. While Heathcliff represents the raw, physical and arguably sexual side of love as a force of nature, Catherine represents love as an ethereal, existentialist energy that surpasses time and circumstances.
This is because, as their upbringings indicate, the horrid abuse and abandonment experienced by Heathcliff contrasts dramatically with Catherine's comforting and peaceful childhood. It comes to no surprise that, as adults, each of their views on life are so dissonant if they are based out of their experience.
When Catherine chooses to marry Edgar more for convention than for love, she is faced with the question on whether Heathcliff means anything to her. For this reason she says the phrase:
"I am Heathcliff"
If love were to shift from the physical-emotional state to a separate, cosmic plane, it is arguable that the souls, or else the most intense sense of "self" that exists within each involved in the relationship would blend into one. This is the basic gist of the phrase. Catherine is attesting to the fact that the connection between herself and Heathcliff is so intense that they have fused into one much like, in a marriage, two people become one.
..he's more myself than I am. Whatever our souls are made of, his and mine are the same
If instead we examine the phrase from a historical perspective, the fact that Bronte's was a male-dominated society implies that, in any love relationship, the woman would have to give herself up and renounce her identity to share that of her husband. Notice that she does not say "Heathcliff is Me"; the preferential treatment of men shows the tendency to place them before the female.
Therefore, the love of Heathcliff's and Catherine's is the combination of two complementary, yet opposing forces, that make the ultimate fusion of two loves into one.