Becoming refers to becoming human. Mia and the Low Men (Can-Toi) share this term. To Mia, "Becoming" was the process of transforming from a creature of the Prim into a being of flesh in blood. To the Can-Toi, "Becoming" refers to them believing they are becoming human (hence the masks they wear). However, a Can-Toi can not have human emotions, so they will never truly be human, but one Can-Toi named Trampas was the closest, and because of this he developed dandruff.
King also used this phrase in his novel The Tommyknockers, but in a reverse sense; there it referred to the change in the population of Haven, Maine gradually shift from their human state to "become" aliens, under the influence of a spaceship that crashed in their town long ago.