What makes spaces what they are is the ability to specify some rooms as belonging to a space, in the sense of a collection. Since spaces are just rooms, this includes other spaces as well (which are then called subspaces). This allows building a tree which can be used for e.g. representing a company hierarchy. A single room can also be a part of more than one space.

Spaces also have the concept of members. Soon support will land for the ability to restrict room joining to the members of the space a room belongs to. This will make it possible to use this as an on-boarding tool. For instance when an employee joins a company, they'd get invited to a company space, allowing them to see all rooms therein and join the ones they need.

There's also a distinction between public and private spaces. Private spaces can be used purely as a tool for personal categorization. This still needs to be supported server-side so that you can have the same view on all your clients.