Dhan means wealth and trayodashi is the 13th day of the weaning moon in the month of Ashwin. Thus, on the day of Dhanatrayodashi all the sources of wealth are worshipped. Apart from this, Dhanatrayodashi is taken as a day to learn from the experience of one’s past deeds and pay homage to memory of ancestors from whom one inherits these traditions.
The farmers worship their cattle and their weapons. Women buy something in metal especialy silver, good for the house. On this day, doorways are hung with torans, garland made of mango leaves and marigolds and decorated with Rangolis drawn to welcome guests.
On this day, Dhanvantari, the God of health and welfare is worshipped by performing acts such as cleaning the entire house, buying new clothes, new vessels etc. Shri Dhanvantari is worshipped on this day because this is the day that he arose from the ocean during the famous Samudra Manthan. The God of Health is worshiped first because Hinduism gives tremendous importance to physical well being.
(Source: http://www.diwalifestival.org/dhanatrayodashi.html)
It is also believed that On the day of Dhantrayodashi, Goddess Lakshmi came out of the ocean during the churning of the Milky Sea. Hence, Goddess Lakshmi, along with Lord Kubera who is the God of wealth, is worshipped on the auspicious day of Trayodashi. However, Lakshmi Puja on Amavasya after two days of Dhantrayodashi is considered more significant.
(source: http://www.drikpanchang.com/festivals/dhanteras/festivals-dhanteras-puja-timings.html)
You can also check this post by my blogger friend – Swapnil Pandey. She is an amazing writer and shares lot of informative stuff.
On this occasion of Dhanatrayodashi/Dhanteras, I wish you an your families that may Lord Dhanwantari bless you with abundant health and may Goddess Laxmi bless you with lot of wealth.
Happy Diwali!!!