First, you'll get relatively little REM-sleep (and as such, you'll dream less), since you'll be missing out on the longer REM periods that you normally experience after about 6 hours of sleep.
If you keep up this pattern, however, you'll get REM rebound to prevent a shortage of REM sleep. This means you'll enter REM sleep sooner than normal and a bigger part of of your sleep period will consist of it.
By doing this, people may optimize their time spent awake, by sleeping for short periods of time (less than half an hour) that consist more or less completely of REM-sleep, so they only have to sleep for about 5 hours in a 24 hour period. This is called polyphasic sleeping.