Compassion is a word that I read in Buddhist and American-Buddhist writings but not so much in Christian language. The Christians tend to use the word "love" and urge love and support and assistance and sympathy with your neighbor and others. But I think much of the result is the same, whether I love or have compassion. Depending of course on what I mean by the two terms. The process of loving or of having compassion can start from different places.
I can tell myself that I should love and bring myself up short when I find I am ignoring another or being annoyed by another. I can just leave a red flag in my mind, like a road worker with a big red sign that says "Stop!" When I see that inner marker, I can take grab myself by the lapels and demand loving and supportive behavior from me toward another.
We did learn in Sunday school to walk in another's shoes, to experience that pain of his rejection, of her fear, of his sadness and take appropriate action to lessen those pains and console the rejected, bolster the afraid and cheer the sad. But life experience as well as literature, drama and poetry, in school and out, gives us sharper, faster and more complete ability to know what the negatives and positives of life feel like from inside. We get better at the human skill of reading faces, voices and bodies to detect not only the basic emotions but some of the poignant details that make individual situations especially strong and deep.
Over time, maybe also as a result of aging, I get faster and more efficient at seeing myself as described in an article about myself. My actions may not be honorable or exemplary but they are understandable. If I step out of my shoes and stand a little distance from myself, I can see that I am afraid and so reacted negatively. I am less inclined to grab lapels and more inclined to offer a cup of tea to myself.
Two valuable guides to better, faster and more effective compassion toward myself are Kristin Neff (books and YouTube) and Brene Brown (books and TED Talks). Neff wrote just the other day about the difference between trying to bolster my feelings about myself with pride or with putting others down as compared to sympathetic but clear-eyed understanding, such as a coach might have. More and more, evidence is building that tenacity, employed intelligence, resiliency as well as empathy and understanding of others comes better from learning self-compassion. The right sort of loving, tender care and appreciation produces stronger soldiers and police dogs, too, as opposed to mere deprivation and meanness.
You guessed it: self-compassion is improved with regular meditation.