Cloud hosting is just running software and storing data on someone else's data centers, rented when you need them, instead of on servers you own and maintain. "The cloud" is not mysterious. It is professionally managed computers in large facilities that you reach over the internet.
The advantages are elasticity and freedom from hardware. You can grow from ten users to ten thousand without buying servers, and you never patch, cool, or replace a machine. You pay for what you use.
Cloud hosting is the foundation that SaaS runs on. It is what lets a software provider grow right alongside its customers, and it is what lets a small business tap into powerful infrastructure it could never afford to build and run on its own.
The trade-off is trust. Your data lives in the provider's facilities, so their security practices, their reliability, and their data policies become part of your own risk picture. The good news is that a reputable cloud provider usually offers far stronger security and uptime than a small business could ever manage alone.