Her husband was in the military and in his memory, she got part of his ‘if I don’t come home’ letter tattooed on her. It says, “Just remember, no matter what, that I love you more than any other person who has ever been loved. Never doubt that.
For anyone who doesn't "get" it, I believe the anchor represents everything in your life that works against you and tries to bring you down. While the quote clearly states you aren't willing to allow those things to sink you.