Design patterns are basically developed to solve complex problem or in other words we can say that they are used to prevent your solution to become complex. They provide us the flexibility to add new functionalities in future without making much changes in our existing code. Open for extension, closed for modification.
Command Pattern basically encapsulates a request as an object and thereby letting you parameterize other objects with different requests and support undoable operations.
When we see a remote control that is a best example of command pattern. In this case we have associated a concrete command to each button and that command has an information of the receiver to act upon.
In your example of switch case, suppose if you want to associate a button on remote control to fan instead of light then again you will have to change the existing code because you need to associate a button with a command. This is the essence of command pattern where it provides you a flexibility to associate any command with a button so that at run time you can change the functionality. Although in general TV remote you don't have this feasibility i.e. you can't make volume up button to work as volume down. But if you use any application to control your TV then you can assign any button any of the available command.
Further, using command pattern you can have a set of commands for a particular functionality to achieve, i.e. macro command. Hence if you think at a broader level then this pattern can get you the flexibility to extend functionalities.
Command pattern help us in decoupling invoker(remote control) and Receiver (Light,Fan,etc) with the help of command object(LightOnCommand, FanOffCommand, etc).
