Squares have long been a feature of London.
A few, such as Trafalgar Square, were built as public open spaces, like the squares found in many cities, known as a plaza, piazza, platz, etc. Most, however, were garden squares, originally built as private communal gardens for use by the inhabitants of the surrounding houses. This type of space is most prevalent in central London, but squares are also found in the suburbs. Some of these gardens are now open to the public, while others, for example around Notting Hill, are still fenced and private.
"Square" is a generic term for these urban open spaces; some are not actually square, or even rectangular. One reason for this is the use of a local nickname for the street, park or garden in question. Another is that some older squares were irregularly shaped to begin with, or lost their original layout due to the city's many transformations, not least following the Great Fire of London and The Blitz.
Each London Borough has rules which have been drawn up prevent inappropriate street names being used to designate new developments or to rename existing features — the general requirement for new squares in London is that they be rectangular and be to some extent open. Billiter Square, EC3 and Millennium Square, SE1 are examples of squares which do not satisfy these guidelines.
Some are entirely paved (Granary Square), while others are almost completely grass and trees (Russell Square). Some have the word "square" in their name, while others do not. Increasingly, spaces are being constructed that are legally private, although in practice open to the public (Paternoster Square). At the other extreme, London's growth over the centuries has encompassed several village greens such as Newington Green, which serve as council-run open spaces in the midst of dense housing. This category of urban green space then begins to shade in to the parks for which London is justly famous.