Paan was invented by Scholars of Aruvedas with the help of Dhanvantari thousands of years ago after taking experiment on rats. Paan was found out good for digestion Even reference of Paan is found in Shrimad Bhagavatam as Lord Krishna used to chew. This evidence is of 5000 years ago.
The tradition of eating Paan was popularised by Queen Noorjehan, the mother of King Shahjehan who built the world famous Taj Mahal for his Queen.
In olden days women used natural elements for makeup and cosmetics. Queen Noorjehan discovered that by adding some particular ingredients to the Paan and eating it gives a beautiful natural red colour to the lips. So along with it's taste the Paan was eaten by women for reddening the lips.