The Cloud is a trendy name for a program or service that is built on top of web sites.   For example Office365, Googles G Suite, Shopify, and Amazon are cloud services.

If you use these services to create a spreadsheet in a web browser, this is on a cloud service. Or, your photo library that you can browse on your phone or your computer through a web browser is another example of a cloud service.

Moving your business to the cloud is about moving from traditional services like retail, and recreating it in an eCommerce Cloud Service like WooCommerce, or Shopify.  You can also create your own cloud service.  A web site that is managed by a CMS is also an example of a cloud service, just like WebShopToolbox.com.
There is no single definition of what a cloud service is, or how it works. There are good cloud services and horrible cloud services. There are a lot of snake oil sales people, so buyer beware of what you are committing to when contracting a service like this.