Trafalgar Square is an open public space in central London. At the centre of this square is Nelson's column guarded by 4 lions. There are also various other sculptures and water fountains around. The name of the square commemorates Battle of Trafalgar as a victory by British Navy against French.
For many many years, new year celebrations were arranged here which was replaced by London Eye since 2005. As said, this is a open space, so there's always crowd in this place. Ideal time to visit is before 9.00am if you want to take a decent photograph.
This picture was taken during the Christmas from western side of the fountain with the National Gallery building at the backdrop. The glowing Christmas Tree (Norway Spruce) is presented by Norwegian Government every year as a token of gratitude to Britain for their support during World War II. Currently one can see 2012 Olympic countdown clock in the square.
There's always a famous square or piazza in every european city. What Trafalgar square depicts is the lifestyle of London, the glory of Britain and the face of true metropolitan/commercial life. It's a place to relax, grab a coffee and watch people. It's a place you cannot miss if you visit London!