In this presentation, we examine the important role of immersive interactive display spaces in supporting data analysis and sensemaking activity. Why is the large physical space offered by immersive displays, both 2D and 3D, important to human sensemaking? How are large spaces fundamentally different from traditional displays when used for sensemaking? How do they help with analytical processes? What is the relationship between display space and computational AI and analytics? How should we design large interactive spaces to maximize human+AI sensemaking performance? We examine how physical space plays fundamental roles at several levels in sensemaking: embodied visualization, embodied interaction, embodied cognition, embodied computing with AI/ML algorithms, and embodied collaboration. Our synthesis of these roles will help illuminate a path forward for future research in immersive analytics and advancing human sensemaking capability in a data-intensive world.