Now, I don't mean this in a loner kind of way...
Think of it like this: "If you always remember that (you are your own best friend), you will always have someone there with you."
I'm taking this right from my favorite blog, A Cup of Jo. She--meaning "Jo," my favorite blog writer--wrote a blog on Mindy Kaling and the Mindy Project (great show, btw), and how this paragraph from a New York Magazine article stuck with her:
"My relationship with my mom is really the single most profound relationship that I’ve ever had in my life," Mindy tells me...But her voice breaks when she starts talking about how she sat down with a pen and paper and asked her mother to give her all the advice she could possibly give her before she died, and Kaling realized she’d never be able to ask her mother for advice again. “I said to her, ‘Mom, I’m going to be so lonely without you.’” She’s crying now but keeps going. “And she just said, ‘You have to be your own best friend. If you always remember that, you will always have someone there with you."