The $J directive controls whether typed constants can be modified or not. In the {$J+} state, typed constants can be modified, and are in essence initialized variables. In the {$J-} state, typed constants are truly constant, and any attempt to modify a typed constant causes the compiler to report an error. 

Writeable consts refers to the use of a typed const as a variable modifiable at runtime. For example:

const
       foo: Integer = 12;
    begin
        foo := 14;
    end.

With $WRITEABLECONST OFF, this code produces a compile error on the assignment to the foo variable in the begin..end block. To fix it, change the const declaration to a var declaration. 

In early versions of Delphi and Object Pascal, typed constants were always writeable, corresponding to the {$J+} state. Old source code that uses writeable typed constants must be compiled in the {$J+} state, but for new applications it is recommended that you use initialized variables and compile your code in the {$J-} state.