The Battle of Trafalgar took place on the 21 October 1805. It was fought by the Royal Navy against the combined fleets of the French and Spanish Navies, during what was known as the War of the Third Coalition that took place between August–December 1805 within the wider Napoleonic Wars (1803–1815). Trafalgar was the most decisive naval victory of the war when twenty-seven British ships of the line were led by Admiral Lord Nelson aboard his flagship HMS Victory. The British defeated thirty-three French and Spanish ships of the line under the French Admiral Pierre-Charles Villeneuve in the Atlantic off the south-west coast of Spain, just west of Cape Trafalgar. The Franco-Spanish fleet lost twenty-two ships in the fight while not a single British vessel was lost. The British victory dramatically established Britain's naval supremacy and was achieved in part through Nelson not adhering to the prevailing naval tactics, which involved engaging an enemy fleet in a single line of battle parallel to the enemy hit each other with broadsides. Nelson instead divided his smaller force into two columns which he then ordered to sail at right angles against the larger enemy fleet and so won the battle. At the height of the battle Nelson was shot by a French musketeer and died shortly after, becoming one of Britain's greatest war heroes.
If you think you may have had ancestors that served in the battle The National Archives has a great portal: http://www.nationalarchives.gov.uk/trafalgarancestors/