We can be very harsh with ourselves - often much harsher than we might be with a friend or a loved one. Self-compassion is an important antidote to our negative self-talk and self-criticism. It is about recognising that you, like everyone else, are not perfect, that you are human and experience suffering too. This is not about feeling sorry for yourself or taking pity on yourself - which can make you feel stuck or like a victim. Some people also worry that self-compassion will make you complacent or self-indulgent - these are myths. It is about having compassion for yourself, being kind towards yourself (warm and understanding towards yourself), being mindful, and validating your experience and emotions.
Unlike self-criticism which asks are you good enough - self-compassion asks what's good for you? - Kristin Neff
In this video A/Prof Kristen Neff - a well-known researcher and practitioner in the field of self-compassion - talks about why self-compassion is important.
Here are two links to loving kindness/self-compassion meditations:
One app I've found useful is 'ACT iCoach', which is free, and under the meditations tab there are a number of 'Loving Kindness' meditations - ACT iCoach on the App Store (apple.com) or in Google Play
Disclaimer: This post is for informational and educational purposes only. It should not be taken as counselling/therapy advice or used as a substitute for such. You should always speak to your own counsellor.