A hug is a way of saying I care about you. It is a way of saying I appreciate you, and I am glad we are friends. A hug is a way of saying what words cannot. At least, there are not words that I can think of at the time that adequately express what a hug does. But I'm not usually so great with words, so maybe it is different for other people.
In my experience, a hug is healing. It can provoke tears that have been locked away, or it can dry tears that have broken loose. A hug is a refresher, a reminder, that can make a person's day and let them know that they are still cared for.
A hug is a greeting; a hug is a good-bye. A hug is a 'I'VE MISSED YOU SO MUCH!' and a hug is a 'So I will see you later this week, right?' A hug is a way to keep someone close to you for just a bit longer. To me, a hug is a 'I am glad we got to share this time together, and I hope to do it again sometime.' A hug is a 'I want to tell you how much I care about you, but I don't know how. So I will do this instead.'
Hugs are how I try to show that I love my family and friends. To me, a hug is a way of showing that I want to know you more, that I care about what you have to say, and that I will listen when you speak.
To me, a hug is not just a movement of the arms, it is a movement of the heart as well.