Let's face it -- we're a codependent society. Most, if not all, of us depend on others to generate our good feelings about ourselves. When we make our spouse or ex-spouse responsible for our self-esteem, we end up with "other-esteem" instead. Without realizing it, many of us allow a relationship to erode our good feelings about ourselves. We give up on interests we personally enjoy or ignore important "growth urgings" to keep peace in our relationships.
All of this is detrimental to your self-esteem. Add to the mix your negative (false) core beliefs from childhood -- which could be triggered by a bad marriage (emotional and/or physical abuse, infidelity, alcoholism, etc.), or religious or community morality -- and you can really believe you're worthless. Even if your divorce was amicable, you might feel like a failure because you couldn't make the marriage work.
Why be concerned with self-esteem? For one, your children learn by observation. When you treat yourself disrespectfully or allow others to do so, you're sending a clear message to your kids: "I don't deserve to be treated well. Feel free to disrespect me as much as I disrespect myself." People with healthy self-esteem don't allow others to abuse them. If your self-esteem is low, it will affect how you are treated on the job, by future love interests, and even by friends and family who profess to love you.