The representation of reaction mechanisms using curved arrows to indicate electron flow was developed by Sir Robert Robinson in 1922. Organic chemists use two types of arrows within molecular structures to describe electron movements.  Single electrons trajectories are designated with single barbed arrows, whereas double-barbed arrows show movement of electron pairs. The arrows tail is drawn at either a lone pair of electrons on an atom or a bond between atoms, an electron source or area where there is relatively high electron density. Its head points towards electron sinks, or areas of relatively low electron density.
When a bond is broken, electrons leave where the bond was; this is represented by a curved arrow pointing away from the bond and ending with the arrow pointing towards the next unoccupied molecular orbital. The electrons can be transferred to a specific atom or can be transferred to a single (sigma) bond, thus making it a double (pi) bond, but the arrow is always pointing towards a specific atom, because electrons always move to a new atom whenever they are "pushed". Organic chemists represent the formation of a bond by a curved arrow pointing between two species.
For clarity, when pushing arrows, it is best to draw the arrows starting from a lone pair of electrons or a σ or π bond and ending in a position that can accept a pair of electrons, allowing the reader to know exactly which electrons are moving and where they are ending.  Bonds are broken in places where a corresponding antibonding orbital is filled. Some authorities allow the simplification that an arrow can originate at a formal negative charge that corresponds to a lone pair.  However, not all formal negative charges correspond to the presence of a lone pair (e.g., the B in FB), and care needs to be taken with this usage.