Благодарности are just props. Ты give them to someone when Ты feel they've done или accomplished something. They serve no real purpose otherwise. Personally I find them useless, which is why I don't have any.
Just go to a person's Профиль and click on their wall. After doing so, Ты should see a благодарность button near the emoticon button and the bottom left of the wall. Click on that and then you'll have an option of giving people all sorts of props. You're welcome.