Curved arrow formalism is an arbitrary convention adopted in the written representation of reactions in organic chemistry. When writing out any reaction, say:
     ..     ..          |         ..
 H - Cl: + :O  - H --> :O  - H + :Cl:
     ..     ..          ..        .. which the dotted straight arrow I've drawn indicates reaction progress, and I've included all Lewis dot structure, I could also draw curved arrows to indicate the movement of electrons. I won't draw them in here, because the ASCII is simply beyond me, but in this reaction two things happen: an H-Cl bond breaks, so that an electron pair previously held in common moves towards the Chlorine atom, and a lone electron pair from the Oxygen atom moves towards the Hydrogen atom which had been bonded to the Chlorine, forming an O-H bond. These two movement of one electron pair could each be represented by curved arrows, where the arrow arises at a letter, representing an atom, or a dash, representing a bond, and the arrow head arrives at another letter or dash. All arrows are drawn on the left side of the reaction diagram, before the straight arrow representing progress. And the curved arrow's head is drawn with two prongs:


when it represents the movement of an electron pair (which is usually), and with one prong:


when it represents the movement of only one electron.

So, when filling in the curved arrows for this reaction (say on an exam) I would draw two curved arrows, each with a two pronged head, on the left side of the straight arrow. One would start at the "O" and end at the leftmost "H", and one would start at the dash between the "H" and the "Cl" and end at the nearby "Cl".