EMDR stands for Eye-Movement Desensitization and Reprocessing.
This treatment technique has this name because when EMDR was first developed, a primary tenant of EMDR involved having a person move their eyes back and forth while visualizing events in their past.
Since then, various other techniques that do not involve direct eye movement have been developed to garner the same effect and results. So, EMDR is a bit of a misnomer today as it implies eye movement is a required part.