If you're curious about where the Square got its name from, it's actually from the Battle of Trafalgar in 1805. Even though Britain won, Admiral Lord Horatio Nelson was killed in the war. His contribution was celebrated by erecting Nelson's Column, which is an important feature of the location.
John Nash redesigned the location and had it reopened in 1844. Across centuries, the place has seen a lot of demonstrations, protests, as well as large events. The location has also been used in TV shows and movies. So, it's no wonder that it has such a thriving social life.