Beards are sticky membranes that the mussels use to attach themselves to stable surfaces in their environment. While most cultivated mussels already come de-beared, from time to time you'll find a couple of stubborn beards still hanging around.
When you find a beard, use a tweezer to grasp it and pull downwards towards the hinged end of the mussel.
Pull firmly until it comes out and discard.
Once finished you should be left with a perfectly cleaned mussel that's recipe ready!