A curly arrow is an arrow that shows the movement of electrons in organic chemistry.
If the arrow is a full headed then it shows the movement of two electrons in normal chemical reactions. If it is a half headed arrow then it shows the movement of one electron you tend to see this in reactions of free radicles.
Make sure that when you are drawing curly arrows they do have a curve in the I know it sounds silly but it is one of the more common mistakes when drawing reaction mechanisms!