First, note that there are no verbs in this poem, making it only a juxtaposition of two images. I use that word, juxtaposition, not to be pretentious but to convey a sense of visual placement, as if the poet were a painter and these images are visibly beside each other as if in a painting. The semicolon is an interesting choice. Given that Pound described this poem as an equation, and that the semicolon can be used to (somewhat paradoxically) link related, independent clauses, it functions as an equal sign, providing two ways of expressing a similar thing. Whereas 2 + 2 and 4 are figures or symbols that express the same "quantity," the "apparition of these faces in the crowd" and "petals on a wet, black bough" express a similar "quality."
There are no linking words such as the simile links "as" and "like." Pound was trying to focus on the images themselves, making the leap from one image to another, making the leap from faces to the petal metaphor a leap of imagination; not a leap that is literally spelled out on the page as if it were a technical manual. As there are no verbs, nothing "happens" in the poem; unless you consider the work of the equation as the work - in other words, the imaginative leap that the poem encourages.
The poem is a hokku, the precursor to the more widely known haiku. Hokku was often an introduction to a longer poem but could also be a pairing of images, usually with no linking words. This is called parataxis. With respect to this poem, it is often referred to (by Pound, I think) as super-position; one image "on top" of another. "On top" is tricky wording. While they are paginated one above the other, think of the abstract nature of a numerical equation; one is not necessarily above, below, to the right; etc. 2 + 2 and 4 are concepts and therefore meanings that are related but that relationship is not relegated to certain spaces in space and time. They just are: related but independent. In physics, superposition refers to a particle that can be in two places at one time; again, somehow beyond space-time.
As for the words themselves, it is open to the reader's own semantic interpretation. But I think it's clear that apparition (ghost, and suddenly "appearing," French), faces - petals, and wet, black bough is a rainy backdrop. Perhaps it is a gloomy, yet somehow inspirational vision of the sudden "equating" of a ghostly group of beautiful faces before a metro in the rain with the likewise ghostly petals, if those petals are no longer attached to the plant. So, life, or the ephemerality of it, is the connecting metaphor in this interpretation and the poet "sees" this as suddenly (appear, apparition); as a revelation which can be as sudden and abstract as 2 + 2 = 4. The meaning is subjective.