what exactly is "no tax day"?

A few states waive sales tax on given days of the year but all that I am aware of limit the waiver to specific items. General this happens just before the start of school and the items waived are frequently connected to back to school stuff.

A few states waive collection of the state sales tax for back-to-school purchases for a brief period of time, typically one weekend. Most limit the break to clothing below a certain value and school supplies. Others are a bit more generous, adding computers and software to the mix. Less than 1/3 of all states do it, and the number has been shrinking due to budget constraints. Google your state's name and "sales tax holiday" to see if your state participates, and if it does, what the ground rules are.

That's a day in the not to distant future, cause if no one has a job, then there is no tax days ahead, unless we can find a way to impose an income tax on the Chinese, and Japanese.

It is a marketing term with no legal meaning. Perhaps the retailer does not add sales tax to your purchase that day.