Overview
Curved arrows represent electron movements.
Chemists utilize curved-arrow (electron-pushing) notation as a bookkeeping tool to keep track of electron movements (bond breaking and formation) within and between compounds. The notation helps in understanding complex reactions, predicting products for an unfamiliar reaction (e.g., on an exam), or even how to exploit a reaction for industrial or medicinal benefits (e.g., selective radiolabeling).
Basic rules of curved-arrow notation
The arrow starts at an electron source (a bond or a lone pair). In other words, the tail of the curved arrow shows where the electrons originate.
The arrow points to where the electrons are heading.
A double-barbed arrow shows the movement of two electrons. A single-barbed arrow shows the movement of one electron. (Below, all examples utilize doubled-barbed arrows.)
Examples
Don't try to memorize these scenarios; just get a solid grasp on reading and interpreting what the curved arrows are trying to convey.