curved-arrow notation
Curved arrows are the grammar of organic chemistry — the way chemists draw a sentence about what the electrons are doing. Each curved arrow is a little movie of one event: a pair of electrons leaving where they are now and arriving somewhere new. The tail of the arrow sits on the electrons that move (a lone pair or a bond), and the head points to where they end up (toward an atom to make a new bond, or onto an atom to become a lone pair). Read the arrows in order and you have read the whole mechanism.
The single most important thing to get right: a full-headed curved arrow shows the movement of a pair of electrons, not the movement of atoms. When you draw an arrow from hydroxide's lone pair to a carbon, you are saying those two electrons swing in to form a bond — the oxygen atom comes along for the ride, but the arrow is tracking the electrons. There are two basic moves. A lone pair can reach out and become a bond; or a bond can break, its electron pair folding back onto one atom. Arrows always start at electrons (never at a positive charge or an empty orbital) and always point toward the electron-poor place those electrons are heading.
Why this matters: arrow pushing turns memorization into prediction. Once you can place arrows correctly, you can take a nucleophile and an electrophile you have never seen together and reason out the product, because the arrows must conserve electrons and charge. They also keep you honest — if your arrows do not balance, your mechanism is wrong. This notation is the shared language every later topic is written in, from substitution to aromatic chemistry.
One arrow from a hydroxide lone pair to the carbon, a second arrow from the C-Br bond onto bromine: that two-arrow picture is the entire mechanism of OH- + CH3Br -> CH3OH + Br-.
Arrows track electron pairs moving from electron-rich to electron-poor, conserving charge.
The classic beginner error is drawing an arrow from a positive atom or an empty orbital. Arrows always start at electrons and point toward where they go — never the reverse. A carbocation does not push; it gets attacked.