Moving parts of your business IT infrastructure to the cloud allows you to scale up (or down!) quickly and dynamically. When a service exists in the cloud, rather than on-premises, additional resources can usually be added at short notice.
Briefly put, "the cloud" refers to someone else's computers. These are powerful machines owned by Microsoft, Amazon, several hosting providers, and us. We use the capacity to provide services to many different customers - because the resources operated by cloud companies are far in excess of what individual companies want to use, we can quickly provision resources for our customers.