A Dandy brush is typically a harder/stiffe bristled brush that helps you remove the heavier build up of dirt, hair and anything else from the coat. You may have already loosened the thick of dirt and hair etc using a Curry Comb, the Dandy brush does a good job of picking this up. Brushes are used by following the direction of the Horses coat (the direction of which way the hair lies) in short strokes lifting the dirt and hair away, working from the front of the Horse towards the back.
The most Dandy Brushes these days ar emade with synthetic fibres which do a great job and do generally probably last longer. Some of the high end brushes are made using natural materials such as rice stems. You would not usually use a Dandy brush on the face of your horse, generally they just dont like them because of being a stiff brush, your Horse may also object to using them on their legs.