"The Yellow Wallpaper" lends itself to many different analyses, and so it can have more than one critical approach. One significant critical approach is the Psychoanalytic, which would examine how the unnamed narrator's mental instability leads to her eventual fate. It is heavily implied that any existing mental conditions in the narrator are exacerbated by forced seclusion, and she enters an imaginary world because she can no longer accept the real world.
"I've got out at last," said I, "in spite of you and Jane. And I've pulled off most of the paper, so you can't put me back!"
(Gilman, "The Yellow Wallpaper," csi.cuny.edu)
Her movement from being "herself" to the "other" that escapes from behind the yellow wallpaper is not explicitly included in the text, but is implied by a transition: her need to remove the wallpaper and help the "creeping woman" escape becomes her desire to "creep" around the room without constraint. The implication is that she felt herself trapped not physically but mentally; her husband believed that creative stimulation would make her more ill, but in fact the removal of stimulation caused her to create a mental world instead of accepting the real world. The "other" that she seems to inhabit at the end could be a manifestation of the Id, the unconscious part of the mind that desires to shake off the Ego and Superego; if her Id escaped its mental confines, it could easily cause her Ego to believe that it too had escaped, even though she ties herself to the room, thus wilfully confining herself even more.