It's more than respect, kindness, caring, or even love. It is all those things, and more. It can be felt and shown for strangers, for friends, even for enemies.
To me, having compassion means that I can hear you. I can listen and understand. I can have empathy. I can be supportive.
Being compassionate means mostly that I am there for you, in whatever way possible. It means that small, mundane tasks are done for you, so that you don't need to focus on those things. It means not needing thanks or gratitude or reciprocity.
Compassion means that I respect you autonomy, your choices, your decisions. Compassion means that judgment is not passed, lectures are not given, disapproval is not expressed. Compassion is something that we all need more of, to give more and to receive.
Compassion is unreserved.