This is kind of hard to explain but hopefully this will make sense.
The article is saying that you need to adopt a different mental approach to keep your self-esteem high. You should stop feeling bad about yourself and stop comparing yourself to others. When they say, "It is not about being better than others, it is about being as good as you can be." They are saying that the main point is NOT to be better than others but to be as good as you can be.
Here are some other examples:
"It's not about if you win, it's about doing your best." This means, it does not matter if you win, what matters is if you did your best or tried as hard as you can.
There is a slang term many people use where they say, "I'm not about that life." For example, if someone told you that they love to drink alcohol but you never drink, you could say, "I'm not about that life."
I hope that makes sense. I can give you more examples if you need them.
As for "...it is about being as good as you can be, period."
The dot ( . ) at the end of a sentence is called a "period." When someone says or writes out the actual word "period" they do it to emphasize what they have said. In this example, they are saying that "being as good as you can be" is very important for you to understand and you should not question it.
Here are some other examples.
If a child is being bad, a parent might say, "I am your parent and you will listen to me, period." This means that the parent's word is very important and should not be questioned.
Or maybe someone who feels that the law is very important might say, "If someone does something illegal, they should go to jail. Period." This means that this is their belief and you shouldn't question it.
Let me know if you have any questions!