I didn't know it was called a symbol. But to explain it:
classes can have what is called an instance variable. Every version of that class you make (for instance, the game_actor class) will have it's own set of those instance variables. By default, only that particular instance of the class can access its instance variables (only arshes can see his HP, MP, Strength, etc. No menu would be able to change or even SEE those variables) Adding
attr_accessor :hp
will allow other classes to read and change the actor's hp instance variable. This makes battle, as well as menu scenes possible. If you DON'T use that, you can't really do anything other than call methods which change the actors variables (think "def changehp").