The notion is closely associated with the theory developed by Henri Lefebvre. He formulated the theory of space as a social product which implies that space is actively created and constructed by social life, practices, symbols, institutions, power relations and daily habits.
According to Lefebvre’s theory, space consists of three components:

Conceived Space. The way space is understood and envisaged by authorities, city planners, architects and other relevant structures or players.

Perceived Space. The reality of the existence and representation of the space that can be experienced by its inhabitants.

Lived Space. The meanings, feelings, memories and emotions that people attribute to this space.
Conflict occurs when the above mentioned three spaces do not overlap.
Take the city center square as an example of the different meanings the space possesses:
From the perspective of authorities, the square is a strictly formal civic place.
At the same time, vendors see it as a great money-making opportunity.
And young people are likely to use the place for socializing.
Protesters will use it as a venue for protests.
While businessmen see the area nearby the square as a perfect place to set their business.
The police look at the square from the viewpoint of the necessity for controlling it.
Thus, at least five meanings of the same space are presented here.
As research has shown conflicts might occur due to the lack of the same understanding of the square and its significance for every social group.
It is also noteworthy to mention that contestation does not mean conflict.
It presupposes a number of stages:
negotiation → resistance → appropriation → exclusion → regulation → protest → reclamation
People residing in cities have an opportunity to exploit their space contrary to the vision of the planners. Such a situation can be illustrated by Hyde Park in London where multiple claims to the square are made by three major groups: civil groups, heritage agents and advocates of the freedom of speech.
Main idea: Right to the City
Lefebvre argued that the concept of the right to the city is at the core of his theory meaning that the cities should belong to the inhabitants and not to those having power over constructing the space.