The historical, ancient city of London until after medieval times was the area within the city walls: basically the area that the Romans colonised and called Londinium, although there was a small Royal/Church presence at Westminster about 3-4 miles westwards along the river from there. As a side note, the area of London that originally fell within the city walls is now the financial district and is still called "The City".

Once London finally started growing too large to be contained within the ancient walls, a natural development was to follow the river towards the great abbey at Westminster and the royal courts there. Being west of the City this region gradually became known as the West End, the East End for a long time being a run-down residential area of slums, sweatshops and the dockyards, although it is considerably improved these days.

Today's modern West End isn't a precisely-defined region within London. It certainly encompasses the theatre district of Soho and nearby Chinatown, but it also includes shopping areas such as Oxford Street, Regent Street and Carnaby Street. Many people would also include the Royal Parks and Buckingham Palace as part of the West End, although others wouldn't. Like I said, it's a fairly loose definition, generally meaning "that part of central London which isn't the City".