Cloud storage is digital storage made available to you through the internet, as opposed to storage you would have locally. Files stored in the cloud (see below) lives in servers (read: computers) in data centres (read: bit barns) anywhere on Earth. Files stored locally would live on the storage inside your computer, or the SSD attached to your computer using USB.
The cloud is a colloquialism often used very broadly to describe many services available through the internet. We'll strive to avoid this type of sweeping over-generalization on Majorcord.