Mary Louise Pratt, in Arts of the Contact Zone uses this term to refer to social places where cultures meet, clash and grapple with each other, often in context of highly asymmetrical relations of power.
Contest itself means to engage in competition to attain power, therefore contested spaces are disputed spaces. To put it in simple terms I see contested spaces as an area where there is a persistent struggle over, with two parties or more to simply gain power. Spaces however become contested spaces when there are limitations put on them, limitations in such a way that affect its inhabitants or the people in and around it physically and mentally. Physically meaning that they are probably removed entirely from the space or are constantly harrowed by the dispute because of the third party. Because of the creation of dispute, sometimes public spaces become contested spaces and no more remain open to everyone.
A prime example of this can be the situation in Kashmir where there is a constant power battle between India and Pakistan as to who’s country it rightfully belongs in. coming back to Mary Louise Pratts explanation, the situation in Kashmir, a special place where there is an Indian and Pakistani culture clash all in order to gain power.
Contested spaces are seen a lot in terms of real estate as these spaces primarily revolve around land ownership. It’s not always on large scale like the Kashmir situation but can happen on a reoccurring basis for example when families dispute over who own the bigger share of land.
Dialing it down even more, contested spaces almost always occur between siblings as to which side of the study table belongs to who.