The situation
Napoleon's plans to invade Britain depended on control of the Channel. The combined French and Spanish fleet under Villeneuve sailed from Cádiz, and Nelson was waiting.
The decision
The accepted method was to fight line against line, ship broadside to ship broadside, which usually produced indecisive results. Nelson planned instead to attack in two columns at right angles to the enemy line, cutting it into pieces that could be overwhelmed before the rest could help.
The risk was real: approaching head-on, his leading ships would take raking fire for a long time without being able to reply. He accepted it, and signalled "England expects that every man will do his duty."
What it cost
The plan worked. Twenty-two enemy ships were captured or destroyed and not one British ship was lost. Nelson was shot by a marksman from the French ship Redoutable and died during the battle. Britain's command of the sea went unchallenged for the rest of the Napoleonic Wars.