SQL Server:problema al pasar la variable a un procedimiento almacenado

No declaraste un parámetro, sino una variable local. Para declararlo como quisieras:

CREATE PROCEDURE pOrders (@enteredClientID varchar(20))
AS
    DECLARE @Results table (ClientID varchar(20), Num_orders int);

    SET NOCOUNT ON;

    -- Get all the order from the client
    INSERT INTO @Results
    SELECT ClientID, sum(Num_orders)
    FROM Orders O
    WHERE O.ClientID = @enteredClientID
    GROUP BY O.ClientID);

    -- Insert the orders into the results table --
    SELECT *
    FROM @Results;

GO;

Y para llamarlo:

exec pOrders @enteredClientID = 'ABC123456789'

o simplemente

exec pOrders 'ABC123456789'