What is the purpose of meditation for Buddhists?

Many people (Buddhists and non-Buddhists alike) begin to meditate because a gentle longing arises in them: a longing to know the answer to a few basic questions: who am I, is there something beyond the 3-dimensional world, what is life ultimately about?

This longing propels a person into meditation, because mystics from all traditions down through the ages have promised that if you meditate, you will begin to get a glimpse into the answers to these questions.