Being your own best friend means that you will always be there for yourself, in good times and bad times.
You will always be able to judge any situation to your own best, and you will always be able to celebrate the good things in life, and correct the mistake you make in your life.
Being your own best friend enables you to help you self being better at living your life, because your best friend (yourself) will be able to reflect and analyze upon your dreams and your actions. Being your own best friend makes your life more beautiful and easier to live, since it gets easier to chose wisely in your daily life.
You become your own best friend by listening to your inner first feeling, by acting upon that one, and if it does not work, correct your action. Being your own best friend also means to support yourself, as you would support your own best friend by being constructive, giving new suggestions for new solutions, cheering up when something goes wrong.
You are also your own best friend, when you look forward to be alone with yourself. Spending time with yourself is a good thing to be able to do. You are waking up and you are going to bed with yourself the rest of your life.