“The cloud is someone else’s computer” is a useful joke because it brings an abstract idea back to physical reality. Behind an online service are machines, networks and people operating them.
Cloud computing makes resources available over a network, often on demand. It can help a system obtain capacity without buying and installing all the underlying hardware in advance. Infrastructure, managed platforms and software services offer different levels of control.
Virtualisation and free software have played an important part in this ecosystem, but cloud computing is not one technology or one commercial arrangement. Prices, support and responsibilities vary by provider, service and contract.
It would therefore be wrong to assume that support is never included, or that the cloud is always cheaper. A useful comparison considers the workload, data, operational skills, availability requirements and the costs of moving or leaving.
For an organisation with the right knowledge, cloud services can make growth easier to manage. For another, a different arrangement may be better. My preference is to understand the practical trade-off rather than choose a slogan.