Cast to MyCharacter is basically just casting it to your player character to make sure it is indeed of that type so you can grab variables that are only available to that class. In blueprints just start typing in “Cast to” and it should bring up the available options to cast it to. In this case he is casting to “MyCharacter” which is the name of the blueprint character in the base game types that can be created through the editor for your project.
Basically it is casting the input object/actor to another class and allows you access to its variables. It is a way of checking to see if the object/actor is a subclass or class of the specified type and if so allow you to access its functions and/or properties that are available to be called.
For C++ the call to cast would be Cast<AActor>(Variable) if my memory is correct to cast and see if Variable is an Actor for example. There should be tutorials around with more details on casting.
I hope I explained it well and if anyone else can elaborate on it if needed that would be great. I hope this helps.