Self-compassion is a way of relating to ourselves with kindness. It is different from self-esteem in that it doesn't require us to be (or to be perceived as) special in comparison to others and it is not dependent on our success. Self-compassion recognizes our basic value without reference to how we do or do not "stack up" next to others and irrespective of success or failure.
The number one reason we gravitate towards self-criticism instead of self-compassion is that we believe we need self-criticism in order to motivate ourselves. Does this sound familiar to anyone??? BUT, Neff's research has demonstrated that in fact the opposite is true, that self-criticism actually undermines our motivation because it stimulates our stress physiology.