A cloud connection is one in which the two endpoints (the remote computer you want to control, and the local device you want to connect from) are automatically discovered by RealVNC's cloud service. Cloud connections are quick, secure and seamless - you don't need to configure firewalls and routers, require a VPN, or know any network addresses - but both endpoints must be connected to the Internet. More information.
Cloud connections are the only option for Home and Professional subscriptions.
If you have an Enterprise subscription, you can establish direct connections as well, or instead. A direct connection is one in which you negotiate the network route between the two endpoints, so you must know network addresses and be able to configure intermediate firewalls and routers. On the other hand, endpoints never 'phone home' to RealVNC, so needn't be connected to the Internet at all. More information.