What is a world (global) city?

We must first note that world cities can be of any size.

What sets them apart/places them so high upon the urban hierarchy is their disproportionate importance economically, politically and culturally.

World cities account for 30% of global economic activity.

The elite 'top three' are considered to be London, Tokyo and New York.

Let's look at Tokyo as an example firstly.
Japan is the 2nd wealthiest economy in the world and Tokyo is the centre of this economy.
It is renowned for its modernity and high levels of consumer spending.
Its economic diversity is very important. It is the home to YOKOHAMA the country's leading port and KAWASAKI a centre of manufacturing.

Next, consider New York.
The HQ of the United Nations is located here. Think about the cultural significance of NY. The 'beat' scene of the 1950s, with Allen Ginsberg, and the 'hip-hip' scene of the 1970s which emanated from the Bronx.
-The 1909 planning laws meant that the slums gathering on NY's periphery were cleared. They were responsible for the grid iron system of streets we know today.
-Diverse culture diaspora. New York is well known for its tolerance of ethnic diversity.

London is a very obvious world city.
-Its GDP is greater than both the countries of Sweden and Switzerland
-It accounts for 40% of the UKs GDP
-Consider how well connected London is, with Heathrow, Gatwick and Stansted Airport.
-Home to many TNC HQ, e.g. Canary Wharf