Hello, I find these terms on the internet frequently, but I don’t know what they are. Can someone explain them in detail?
Marek, welcome 
Here’s the simple version:
Vertical scaling (scale up) = making one server more powerful.
You add more CPU, RAM, or storage to the same machine.
Easy and quick — but there’s a hardware limit.
Horizontal scaling (scale out) = adding more servers.
Traffic is spread across multiple machines using a load balancer.
More complex, but almost unlimited growth potential.
In short:
Vertical = upgrade one server.
Horizontal = add more servers.
Most growing websites start vertical, then move to horizontal as traffic increases.