A good question, one that has been considered repeatedly ever since EMDR was developed. There are however of theories, these include:

1. The very specific movements replicate the type of movement we experience when in REM sleep. It is thought that during REM sleep our brain is processing information, hence replicating the same eye movements seeks to replicate that same high speed processing mode
2. EMDR enables gradual desensitisation to the disturbing stimuli by engaging logical thinking patterns at the same time as accessing emotions

Whilst the precise mechanism is uncertain the overall results of treatment are not - EMDR is can be an highly effective tool.