This is from the title of an 1871 book: Through the Looking Glass, and What Alice Found There. It is the sequel to Alice in Wonderland.
“Looking glass” is apparently an early English term for a mirror – a “glass” into which you “look.” So, you look into a mirror to see your reflection, but if you go beyond your own reflection, you go “through the looking glass.”
It can also mean to step into a strange and foreign land, referring to the plot of the book. To go through a mirror has often been a trope to represent entrance into the unknown.