The speaker is trying, and failing, to forget someone she loved two years ago. She imagines erasing him from her mind, then switches to a sharper image: he is like gum stuck under a school desk, and every time she scrapes, small pieces remain and grow back stronger. Even the memory of his cologne has faded, yet she still reaches for it.
When she closes her eyes, she sees his skin, his half smile, and his strong back, which she compares to Atlas holding up the world. She still keeps his jacket, his boxers, and a jewelry box full of his letters, so part of her hasn't let go. The line about first and last loves being tangled together suggests she's confused about where this relationship sits in her life.
The mood is aching and wistful, with a bit of humor in the gum comparison. The ending is quietly sad: she admits he will only love her back in dreams.