My interpretation in popular view of the expression: This is a space that is fully utilized for an expression .
Space as a 1) literal physical place 2) media platforms 3) influential expressions in arts, science, literature, ideas
Means to take your power in a space or spaces because of your strong influence, conviction, believe, persistence, ideas, theories etc.
In short- utilize your strengths because of your input.
Power of space means the ability to strongly influence the literal space, metaphorical space in the way of valuable, generating interest effect. Someone presentation of talent can be a powerful experience.
Take the power of space means that your presence of expression is highly engaging and influential.
Quote definition :" Spaces of power
The notion of ‘space’ is widely used across the literatures on power, policy, democracy and citizen action. In the powercube approach, which is designed as a tool to analyse how power affects citizen action and participation, usually spaces refer to decision-making arenas and forums for action, but they can also include other ‘spaces’ that are seen as opportunities, moments and channels where citizens can act to potentially affect policies, discourses, decisions and relationships which affect their lives and interests. For more conceptual reviews of the concept of spaces, read about academic approaches to the concept of space.

While there can be many such kinds of spaces, in the powercube approach we normally refer to three: closed, invited and claimed spaces."