There are a couple different species commonly seen but all are small (about 1/16 of an inch or smaller).  These reddish brown "flat" worms will appear on the tank glass, the sand, on your corals ... on everything in the tank.
    

Flatworms do not eat or hurt corals but if allowed to grow in enough numbers they can block a coral from getting enough light.  Flatworms have toxins in their flesh that can be harmful if eaten by fish BUT I've found a fish that aren't bothered by them & actually eat them as though they were a delicacy!

The Scooter Dragonet!

A cool little fish that scoots about our tanks always looking for tasty copepods and more to fill their never ending appetite!  The unique fish are not only fun to watch but have proven themselves to be great at eating flatworms too!

Flatworms are usually an indicator of high nutrients in a system.  The best way to remedy them is to siphon out all visible (as much as possible) perhaps a couple times a week (small water changes which also helps reduce the nutrient load).  If you can remove affected corals & rocks, bring them to your sink & quickly rinse with lukewarm water.  They cannot tolerate freshwater & will detach instantly.  Add fresh reef carbon to your system, perhaps even a Polyfilter & be sure your skimmer is operating properly because again, Flatworms thrive in nutrient rich environments.

Try not to fret over Flatworms.  They aren't hurting anything & when the nutrients are lowered, many times they will disappear overnight.