Tinanam, you are referring to the famous "air quotes" or "finger quotes."
When you are writing, sometimes you use quote marks to show that you're using a word in a new, unexpected, or ironic manner. When some people are speaking, they use those little finger quotes the same way.
For example, we recently got a new car - new for us, but used - it is a 2006 model. So if I were talking to someone, I may say something like "We're taking the 'new' car on our trip" and if I were one of those finger-quote people, I may make that little motion while saying the word "new."