The eye movements are roughly related to the dream that the person is having. People awakened from REM sleep are most likely to report a dream. The most important information sought by sleep researches is that there is a regular pattern of alpha waves that occurs every time you sleep. In adults the first period of REM sleep lasts only 10 minutes. Towards early morning REM lasts approximately one hour.
Infants go through a very different pattern than adults do.
Some researches think that REM has a different affect on infants then it does on adults. In NREM the sleep the higher brain center is not as active. The eye movements are either very slow or not there. Body movements are rare and when they are they are oblivious to people. The people who wake from NREM sleep rarely report dreams they had that night.