Cloud systems fall into two types. Private hosted systems and full cloud systems.
With a private hosted system software is installed onto a virtual server and hosted in a data centre and used just by you. No one else shares your PBX. You still have extensions and you still pay for outside lines. This is the equivalent of taking your existing phone system off site.
With a full cloud system you rent extensions and create a system on a shared platform. The advantage is the platform will be backedup across multiple locations and be connected via multiple ISP's. You pay per user on the system, and have a stable system that is maintained an upgraded by a major carrier.