Cloud
The "cloud" is a simple way of saying "somebody else's computer(s)". In years past, you simply ran your applications on your own hardware and infrastructure, connected or isolated by the networking layer. Then it was popular to centralize computing infrastructure into specialized facilities called "data centers" for economies of scale when it came to power, cooling, security, bandwidth, etc. Eventually, virtualization technologies made networking and all the other core infrastructure elements (including hardware, or 'bare metal') controllable in software so that enterprises no longer wanted to manage their own racks, servers, switches and so on in their access controlled 'cages'. The server room turned into a rented service called "the cloud". When you consider that the term includes just about every aspect of computing, there are thousands of companies and technologies that make up the cloud.
There are so many Virtualization technologies. One key demarcation is the difference between a "Virtual Machine" and a "Container". A virtual machine comes as close as possible to running independent hardware while still virtualizing the environment. This means you can run a separate kernel from the host. Meanwhile, a container is achieved by using process isolation in the Linux kernel[1]. So while a container is less flexible, it is also more lightweight.
For Users
For users, there are interesting examples of containerization like the Firefox browser add-on multi-account containers. Since so many services are delivered via the browser, this containerization allows a user to use multiple accounts with the same service provider at the same time. For example, you could use multiple GMail or YouTube accounts at the same time in the same browser. Browsers including Chrome and Firefox offer the concept of 'profiles' to establish multiple personas in the same browser (e.g. 'work' vs. 'personal'). Multi-account containers takes the control and manageability to new levels for each profile. You can automatically segregate categories of browsing activity within your profile: 'banking', 'social media', 'news' and so on. See https://support.mozilla.org/en-US/kb/containers, and the 2017 blog post for more.
SaaS Examples
Then there are a plethora of cloud services such as GMail.
Cloud Providers
The big three cloud providers are Amazon Web Services (AWS), Microsoft Azure, and Google Compute Platform (GCP). Smaller companies like Digital Ocean or Linode can be more user-friendly and less expensive while still offering a wide range of services.
Cloud Administration
There are the system deployment or management tools such as Ansible, Juju, Puppet, Vagrant and VirtualBox which are either cloud-centric or at least cloud-compatible. The large industry players joined together in 2015 to create the CNCF, or Cloud Native Computing Foundation to further galvanize this transition to the cloud.
Minor Example
One example of an early cloud-centric tool that is common to Ubuntu, Fedora, Debian, RHEL, CentOS and more is the cloud-init set of Python scripts.