1. To think something over carefully before saying something; to mull something over.
2. To think about doing something. English = contemplate.
1. Used alone to signal that you are thinking something over carefully and considering what you will say or what your answer to a question will be. English = 'Let me see...', 'Um..', and so on.
1. There is a very similar gesture that is widely used in deaf and hearing communities which is probably related to this sign, if not actually being it's source: one holds one's chin using the thumb and index infer. It is immortalized in Rodin's famous statue of "The Thinker".