A Hug (called "Jaadu ki Jhappi" in Munnabhai MBBS movie) is an expression that takes away all formalities, it gives comfort and it reduces stress in so many situations. It's like an "all izz well" situation in 3 Idiots movie. You hug someone and you say it briefly that you care.. or you are thankful.. or you are there or you understand them.
Honestly, how important that moment is for the other person is not easy to guess but I can promise that it makes a big difference.
I also do not encourage hugging someone you are not comfortable with. I am just saying that many times, if you recall, at the time of saying bye to your close friends or even some other close ones, do you not feel that your heart will feel better if you hug them once? But those times, I have seen it not very easily acceptable to the majority around. I can't get any answer. It just feels narrow minded. I really don't know the thinking on other side... so can't say more.
But in this attached picture, doesn't a hug look like the best expression ever?