The Mirrors are an important feature in Silent Hill: Origins. They are instrumental in controlling access into and out of the Otherworld. When touched, the world around Travis Grady undergoes a transition into the Otherworld. When looked into from the Otherworld side, the normal state of the area is reflected and vice versa.
After Travis Grady's short conversation with Dr. Michael Kaufmann regarding the status of Alessa Gillespie, Travis takes it upon himself to explore Alchemilla Hospital, searching for clues as to the condition of the young girl. Searching Room 205 and finding only a stained gurney, Travis prepares to leave the room, when the young girl he saved appears in the mirror. Rather than being in the same room with Travis, Alessa appears inside the mirror; a warped, bloody, and filthy reflection of Room 205. Pressing her hand to the mirror, she leaves behind a bloodied hand print. Travis, mimicking the girl, presses his own hand to the mirror. As he does, the world undergoes a transformation into its Otherworld counterpart.
As long as a mirror is present, Travis has free reign to jump between the Otherworld and the Fog World. In addition to granting Travis the means to move freely between worlds, the mirrors play an important role in puzzle-solving, as most locked doors in one world become unlocked in the other.
In general, superstition has led to mirrors occasionally being seen as portals to a parallel universe, and this directly connects with the game as when Travis's mother, Helen Grady, was hospitalized in Cedar Grove Sanitarium, she revealed during an interview that on the other side of a mirror is some "otherworld". People within this "other world" were telling Helen that her child was a demon, and he needed to be killed. It was her attempt to do so that led to her committal to Cedar Grove.
In contrast, the nature of the Fog World as a calm and tranquil place and the Otherworld as a cruel and twisted place could be seen as a parallel to Travis himself. Travis looking in the mirrors and seeing the world differently could represent how different the world looks through each side of his personality. Travis constantly switching back and forth could represent his mind fighting for a dominant personality.