Contested in my mind would be a spaces where there is a sense of competition. It can be urban vs rural, historic vs modern.There are two meanings attached to the word contested one being, to engage in competition to attain (a position of power) second, oppose (an action or theory) as mistaken or wrong. So either related in context of space defines a it to be a place or structure of power play. A place of struggle and competition.
When we refer to space there is a question of scale and impact. Contested spaces depending on the scale will have a huge or small impact according to me. For example if we take a courtroom. There are two parties trying to convince a judge who shall decide their fate. Here the impact can be national or global. But spaces like classrooms where the scale is small and the impact is more individual. But in either case I think the scale of the place affects the impact may that be positive or negative.
Contested spaces I think can also be positive because it can have a good impact and bring out the best in people. Places like classroom and wanting to be the best can being excellence in fields like sports or academics. But, in todays time people have gone over board. Space itself have created wars. Space denotes power and money.