What did it mean to great Britain to win the battle of Trafalgar?

A great deal. The French Emperor, Napoleon Bonaparte had invaded and taken over most of the countries in Europe and Britain was fighting for survival. For years the British had been fearful that Napoleon was going to invade and the battle of Trafalgar was the point at which Napoleon's naval power was utterly destroyed by the British navy. This meant that Napoleon could no longer threaten Britain with invasion by sea - which as Britain was an island meant that he was no longer a direct threat. It also meant that Britain could then concentrate on defeating Napoleon on land and ending his tyranny in Europe. This was achieved at the battle of Waterloo.