Consider the book in a few stages: first there is the competition between the suitors Tarr and Kriesler and Soltyk, when they attempt to woo women in France during their time abroad. They represent different parts of the world, quite literally, and so do the women they choose. For instance, Tarr's first fiancee is Bertha, a German woman with a no non-sense policy that prohibits the kind of wonder and romance that Tarr thrives on. He fails to end his relationship with her because he feels shame, but he ends up just doing whatever he wants, because that displeasure makes him desperate for joy.
Then, randomly at the end, we meet two new characters which are probably designed as metaphors or something. Perhaps the reader could view Rose and Prism as an epilogue of sorts, describing the major life phases that Tarr walks through after his breakup from Bertha. The dilemma he never really wanted to solve was always whether he loved Bertha, and then whether he loved Anastaysa, but in both situations, he decides to walk away. After this, he passes through a season of "rose," perhaps an allusion to rose-colored glasses, meaning he is happy for a season.
Perhaps that means that Prism represents a kind of circumspect attention. If Rose brings happiness to him by enchanting him and entertaining his interests, then Prism is a symbol for diversity and depth. If the reader prefers that interpretation, then it would follow here that earlier in the novel when Tarr is messing around with women he doesn't really even care about, perhaps it was because of some unspoken aversion to displeasure. Certainly the fact that he is in affairs with both Prism and Rose are not encouraging signs for his commitment issues.
