The basic idea is that your device that's running the app will send (or "cast") this curated version of the map view to an external display. That could be a TV, projector, computer monitor, or even another tablet or phone, depending on the casting approach.
To that end, we are exploring a couple of different screen casting options. The final technology will come down to a matter of performance, cost (both to develop, maintain, and for the users), and backer choice.
For more detailed information, including the casting options we are currently considering, see Update #17 here: https://www.kickstarter.com/projects/atomswitch/infinitas-dm/posts/1540365