Traditional Day is a day designated for people to come in traditional attire from their home state, or specific culture of their choice. Usually it is connected to Independence Day, and may be observed on a day close to August 15. But this really is a matter of choice for the company management.
So on a typical Traditional Day in a corporate office in a city like Mumbai, the Bengali may wear a kurta and dhoti in Bangla style, a Maharashtrian might wear a saree and accessories in a particular Maharashtrian style, a Malayalee might wear a white shirt and mundu with gold borders. And so on.
Traditional Day is observed as a celebration of India's diverse culture, and is usually relaxed and an easy work day. Especially if you are somewhat uncomfortable with what you are wearing.
For many, it can be a pain in the ass.